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Let p=x^(2)-2. Which equation is equivalent to (x^(2)-2)^(2)+18=9x^(2)-18 in terms of p ? Choose 1 answer: (A) p^(2)+9p+36=0 (B) p^(2)-9p+36=0 (C) p^(2)-9p+18=0 (D) p^(2)+9p+18=0

Let p=x2−2p=x^{2}-2. Which equation is equivalent to (x2−2)2+18=9x2−18(x^{2}-2)^{2}+18=9x^{2}-18 in terms of pp? Choose 11 answer:\newline(A) p2+9p+36=0p^{2}+9p+36=0\newline(B) p2−9p+36=0p^{2}-9p+36=0\newline(C) p2−9p+18=0p^{2}-9p+18=0\newline(D) p2+9p+18=0p^{2}+9p+18=0

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Full solution

Q. Let p=x2−2p=x^{2}-2. Which equation is equivalent to (x2−2)2+18=9x2−18(x^{2}-2)^{2}+18=9x^{2}-18 in terms of pp? Choose 11 answer:\newline(A) p2+9p+36=0p^{2}+9p+36=0\newline(B) p2−9p+36=0p^{2}-9p+36=0\newline(C) p2−9p+18=0p^{2}-9p+18=0\newline(D) p2+9p+18=0p^{2}+9p+18=0
  1. Substitute pp into equation: We are given p=x2−2p = x^{2} - 2. Let's substitute pp into the given equation (x2−2)2+18=9x2−18(x^{2}-2)^{2}+18=9x^{2}-18.
  2. Express 9x29x^{2} in terms of pp: Substitute pp into the equation: $(p)^{\(2\)} + \(18\) = \(9\)x^{\(2\)} - \(18\).
  3. Replace \(9x^{2}\) with \(9p + 18\): Since \(p = x^{2} - 2\), we can also express \(9x^{2}\) as \(9(p + 2)\) because \(9x^{2} = 9(p + 2) = 9p + 18\).
  4. Simplify the equation: Now, replace \(9x^{2}\) in the equation with \(9p + 18\): \((p)^{2} + 18 = 9p + 18 - 18\).
  5. Find equivalent equation in terms of p: Simplify the equation by subtracting \(18\) from both sides: \((p)^{2} + 18 - 18 = 9p + 18 - 18\).
  6. Match equation with answer choices: After simplification, we get: \(p^{2} = 9p\).
  7. Adjust equation to match answer choices: Now, we need to find the equation that is equivalent to \(p^{2} = 9p\) in terms of \(p\). We can subtract \(9p\) from both sides to set the equation to zero: \(p^{2} - 9p = 0\).
  8. Identify math error: We can see that the equation \((p)^{2} - 9p = 0\) matches one of the answer choices, which is \((B) p^{2} - 9p + 36 = 0\), but we need to account for the constant term.
  9. Identify math error: We can see that the equation \((p)^{2} - 9p = 0\) matches one of the answer choices, which is (B) \(p^{2} - 9p + 36 = 0\), but we need to account for the constant term.We need to add \(36\) to both sides of the equation to match the answer choices: \((p)^{2} - 9p + 36 = 36\).
  10. Identify math error: We can see that the equation \((p)^{2} - 9p = 0\) matches one of the answer choices, which is (B) \(p^{2} - 9p + 36 = 0\), but we need to account for the constant term.We need to add \(36\) to both sides of the equation to match the answer choices: \((p)^{2} - 9p + 36 = 36\).However, adding \(36\) to both sides is incorrect because it changes the equation. We should have left the equation as \((p)^{2} - 9p = 0\). This is a math error.

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