Divya is solving the following equation for w. 3w-sqrt(20-5w)=2 Her first few steps are given below. 3w=sqrt(20-5w)+2 3w-2=sqrt(20-5w) (3w-2)^(2)=(sqrt(20-5w))^(2) 9w^(2)-12 w+4=20-5w Is it necessary for Divya to check her answers for extraneous solutions? Choose 1 answer: (A) Yes (B) No

Isolate square root: First, isolate the square root on one side of the equation. 3w = sqrt(20 - 5w) + 2Subtract and isolate: Subtract 2 from both sides to get the square root by itself. 3w - 2 = sqrt(20 - 5w)Square both sides: Square both sides to eliminate the square root. (3w - 2)^2 = (sqrt(20 - 5w))^2Expand and simplify: Expand the left side and simplify the right side. 9w^2 - 12w + 4 = 20 - 5wCombine like terms: Add 5w to both sides to bring all w terms to one side. 9w^2 - 12w + 5w + 4 = 20Set equation to zero: Combine like terms. 9w^2 - 7w + 4 = 20Solve quadratic equation: Subtract 20 from both sides to set the equation to zero. 9w^2 - 7w - 16 = 0Now, Divya would need to solve the quadratic equation for w, but since we squared both sides of the equation earlier, there's a chance we introduced extraneous solutions. So, it's necessary to check the solutions against the original equation.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Divya is solving the following equation for
w.

3w-sqrt(20-5w)=2
Her first few steps are given below.

3w=sqrt(20-5w)+2

3w-2=sqrt(20-5w)

(3w-2)^(2)=(sqrt(20-5w))^(2)

9w^(2)-12 w+4=20-5w
Is it necessary for Divya to check her answers for extraneous solutions?
Choose 1 answer:
(A) Yes
(B)
No

Divya is solving the following equation for $w$ . $\newline$ $3 w-\sqrt{20-5 w}=2$ $\newline$ Her first few steps are given below. $\newline$ $3 w=\sqrt{20-5 w}+2$ $\newline$ $3 w-2=\sqrt{20-5 w}$ $\newline$ $(3 w-2)^{2}=(\sqrt{20-5 w})^{2}$ $\newline$ $9 w^{2}-12 w+4=20-5 w$ $\newline$ Is it necessary for Divya to check her answers for extraneous solutions? $\newline$ Choose $1$ answer: $\newline$ (A) Yes $\newline$ (B) $\mathrm{No}$

View step-by-step help

Home

Math Problems

Precalculus

Descartes' Rule of Signs

Full solution

Q. Divya is solving the following equation for

w

\newline

3 w-\sqrt{20-5 w}=2

\newline

Her first few steps are given below.

\newline

3 w=\sqrt{20-5 w}+2

\newline

3 w-2=\sqrt{20-5 w}

\newline

(3 w-2)^{2}=(\sqrt{20-5 w})^{2}

\newline

9 w^{2}-12 w+4=20-5 w

\newline

Is it necessary for Divya to check her answers for extraneous solutions?

\newline

Choose

1

answer:

\newline

(A) Yes

\newline

(B)

\mathrm{No}

Isolate square root: First, isolate the square root on one side of the equation. $\newline$ $3w = \sqrt{20 - 5w} + 2$
Subtract and isolate: Subtract $2$ from both sides to get the square root by itself. $\newline$ $3w - 2 = \sqrt{20 - 5w}$
Square both sides: Square both sides to eliminate the square root. $\newline$ (\(3w - $2$ )^ $2$ = (\sqrt{ $20$ - $5$ w})^ $2$
Expand and simplify: Expand the left side and simplify the right side. $\newline$ $9w^2 - 12w + 4 = 20 - 5w$
Combine like terms: Add $5w$ to both sides to bring all $w$ terms to one side. $\newline$ $9w^2 - 12w + 5w + 4 = 20$
Set equation to zero: Combine like terms. $9w^2 - 7w + 4 = 20$
Solve quadratic equation: Subtract $20$ from both sides to set the equation to zero. $\newline$ $9w^2 - 7w - 16 = 0$
Solve quadratic equation: Subtract $20$ from both sides to set the equation to zero. $\newline$ $9w^2 - 7w - 16 = 0$ Now, Divya would need to solve the quadratic equation for $w$ , but since we squared both sides of the equation earlier, there's a chance we introduced extraneous solutions. So, it's necessary to check the solutions against the original equation.