Question

In the following equation, determine whether the given values are solutions of the given equation :
$a^2{x}^2-3abx+2b^2=0,x=a/b,x=b/a$

• A. x = $\frac{b}{a}$ is a solution but x = $\frac{a}{b}$ is not a solution.
• B. x = $\frac{b}{a}$ is not a solution but x = $\frac{a}{b}$ is a solution.
• C. x = $\frac{b}{a}$ & x = $\frac{a}{b}$ are not solutions.
• D. x = $\frac{b}{a}$ & x = $\frac{a}{b}$ are solutions.

Answer 1

The correct option is A x = $\frac{b}{a}$ is a solution but x = $\frac{a}{b}$ is not a solution.

Given $a^2{x}^2-3abx+2b^2=0.x=a/b,x=b/a$

Let $x=a/b$ then

$a^2(a/b{)}^2-3ab.(a/b)+2b^2=0$

$=a^2.\frac{a^2}{b^2}-3a^2+2b^2$

$=\frac{a^4}{b^2}-3a^2+2b^2\ne 0$ (Not a solution)

Now, $x=b/a$

$a^2.(b/a{)}^2-3ab.(b/a)+2b^2=0$

$=a^2.\frac{b^2}{a^2}-3ab.\frac{b}{a}+2b^2$

$=b^2-3b^2+2b^2=0$

Hence $x=b/a$ is a solution, but $x=a/b$ is not.