Question

It$\frac{x}{a}+\frac{y}{b}=a^2+b^2$ and $\frac{x}{a^2}+\frac{y}{b^2}=a+b$ then $x=$?

• A. $a$
• B. $a^2$
• C. $a^3$
• D. $a^4$

Answer 1

Answer: (C)

$a^3$

Let $\frac{x}{a}+\frac{y}{b}=a^2+b^2$ -- $\left(1\right)$
And $\frac{x}{a^2}+\frac{y}{b^2}=a+b$ -- $\left(2\right)$
Multiplying eqn $\left(1\right)$ with $b$, we get
$\frac{bx}{a}+y=a^{2}b+b^3$ -- $\left(3\right)$
Multiplying eqn $\left(2\right)$ with $b^2$, we get
$\frac{b^{2}x}{a^2}+y=a{b}^2+b^3$ -- $\left(4\right)$
Subtracting eqn $\left(3\right)$ from eqn $\left(4\right)$, we get
$\frac{b^{2}x}{a^2}-\frac{bx}{a}=a{b}^2-a^{2}b$
Dividing both sides by $b$, we get
$\frac{bx}{a^2}-\frac{x}{a}=ab-a^2$
$\Rightarrow \frac{x}{a}(\frac{b}{a}-1)=a(b-a)$
$\Rightarrow \frac{x}{a}\left(\frac{b-a}{a}\right)=a(b-a)$
$\Rightarrow \frac{x}{a}\left(\frac{1}{a}\right)=a$
$\Rightarrow x=a^3$