Resources

Resources

Bytelearn - cat image with glasses

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

View step-by-step help

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.

More problems from Descartes' Rule of Signs

Question

Find the solutions of the quadratic equation

2 x^{2}-8 x-9=0

\newline

1

\newline

2 \pm \frac{\sqrt{34}}{2} i

\newline

-2 \pm \frac{\sqrt{34}}{2} i

\newline

2 \pm \frac{\sqrt{34}}{2}

\newline

1 \pm \frac{\sqrt{34}}{4}

Posted 3 months ago

Question

x^{3}+7 x^{2}-36

\newline

The polynomial has zeros at

-6

2

. If the remaining zero is

z

, then what is the value of

-z

Posted 3 months ago

Question

x

\newline

Enter the solutions from least to greatest.

\newline

\begin{array}{l} (-5 x+4)(x-3)=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Posted 3 months ago

Question

x

\newline

Enter the solutions from least to greatest.

\newline

(2 x+4)(3 x-2)=0

\newline

x=

\newline

x=

Posted 3 months ago

Question

x

\newline

Enter the solutions from least to greatest.

\newline

\begin{array}{l} (3 x-6)(-x+3)=0 \\ \text { lesser } x=\square \\ \text { greater } x=\square \end{array}

Posted 3 months ago

Question

x

\newline

Enter the solutions from least to greatest.

\newline

(x+6)(-x+1)=0

\newline

x=

\newline

x=

Posted 3 months ago

Question

Is the following function even, odd, or neither?

\newline

f(x)=\frac{3}{x^{2}+2}

\newline

1

\newline

\newline

\newline

Posted 3 months ago

Question

Is the following function even, odd, or neither?

\newline

f(x)=\frac{1}{4-x^{2}}

\newline

1

\newline

\newline

\newline

Posted 3 months ago

Question

Is the following function even, odd, or neither?

\newline

f(x)=2|x|-5

\newline

1

\newline

\newline

\newline

Posted 3 months ago

Question

Is the following function even, odd, or neither?

\newline

f(x)=\frac{x}{x^{2}+1}

\newline

1

\newline

\newline

\newline

Posted 3 months ago