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Miku solves the equation below by first squaring both sides of the equation. sqrt(z^(2)+2z-3)=z-3 What extraneous solution does Miku obtain? z=

Miku solves the equation below by first squaring both sides of the equation.\newlinez2+2z−3=z−3 \sqrt{z^{2}+2 z-3}=z-3 \newlineWhat extraneous solution does Miku obtain?\newlinez= z=

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Q. Miku solves the equation below by first squaring both sides of the equation.\newlinez2+2z−3=z−3 \sqrt{z^{2}+2 z-3}=z-3 \newlineWhat extraneous solution does Miku obtain?\newlinez= z=
  1. Rephrasing the Problem: First, let's rephrase the ＂What extraneous solution does Miku obtain when solving the equation z2+2z−3=z−3\sqrt{z^{2}+2z-3}=z-3 by first squaring both sides?＂
  2. Squaring Both Sides: Miku starts by squaring both sides of the equation to eliminate the square root. The equation becomes (z2+2z−3)2=(z−3)2(\sqrt{z^{2}+2z-3})^2 = (z-3)^2.
  3. Expanding the Equation: After squaring both sides, the equation simplifies to z2+2z−3=(z−3)2z^{2}+2z-3 = (z-3)^{2}. We need to expand the right side of the equation.
  4. Solving for z: Expanding the right side, we get z2+2z−3=z2−6z+9z^{2}+2z-3 = z^2 - 6z + 9.
  5. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.
  6. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.
  7. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.
  8. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.
  9. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.
  10. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.
  11. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955.
  12. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9. Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9. Combining like terms, we get 8z−3=98z - 3 = 9. Adding 33 to both sides gives us 8z=128z = 12. Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900. Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation. However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955. Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977.
  13. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955.Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977.Calculating the inside of the square root, we have 2z−3=−6z+92z-3 = -6z + 988.
  14. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955.Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977.Calculating the inside of the square root, we have 2z−3=−6z+92z-3 = -6z + 988.Simplifying the terms inside the square root, we get 2z−3=−6z+92z-3 = -6z + 999.
  15. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9. Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9. Combining like terms, we get 8z−3=98z - 3 = 9. Adding 33 to both sides gives us 8z=128z = 12. Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900. Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation. However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955. Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977. Calculating the inside of the square root, we have 2z−3=−6z+92z-3 = -6z + 988. Simplifying the terms inside the square root, we get 2z−3=−6z+92z-3 = -6z + 999. Taking the square root of 6z6z00, we get 6z6z11.
  16. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955.Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977.Calculating the inside of the square root, we have 2z−3=−6z+92z-3 = -6z + 988.Simplifying the terms inside the square root, we get 2z−3=−6z+92z-3 = -6z + 999.Taking the square root of 6z6z00, we get 6z6z11.Now we substitute 2z−3=−6z+92z-3 = -6z + 922 into the right side of the original equation, which is 6z6z33.
  17. Checking for Extraneous Solution: Next, we subtract z2z^2 from both sides to simplify the equation, which gives us 2z−3=−6z+92z-3 = -6z + 9.Now, we add 6z6z to both sides to isolate the zz terms on one side, resulting in 2z+6z−3=92z + 6z - 3 = 9.Combining like terms, we get 8z−3=98z - 3 = 9.Adding 33 to both sides gives us 8z=128z = 12.Finally, we divide both sides by 88 to solve for zz, which gives us 2z−3=−6z+92z-3 = -6z + 900.Simplifying the fraction 2z−3=−6z+92z-3 = -6z + 911, we get 2z−3=−6z+92z-3 = -6z + 922 or 2z−3=−6z+92z-3 = -6z + 933. This is the solution we obtain after squaring both sides of the equation.However, we must check this solution in the original equation to ensure it is not extraneous. We substitute 2z−3=−6z+92z-3 = -6z + 922 into the original equation 2z−3=−6z+92z-3 = -6z + 955.Substituting 2z−3=−6z+92z-3 = -6z + 922 into the left side of the original equation, we get 2z−3=−6z+92z-3 = -6z + 977.Calculating the inside of the square root, we have 2z−3=−6z+92z-3 = -6z + 988.Simplifying the terms inside the square root, we get 2z−3=−6z+92z-3 = -6z + 999.Taking the square root of 6z6z00, we get 6z6z11.Now we substitute 2z−3=−6z+92z-3 = -6z + 922 into the right side of the original equation, which is 6z6z33.Calculating the right side, we get 6z6z44.

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