#### Question

In the following, determine whether the given values are solutions of the given equation or not:

a^{2}x^{2} - 3abx + 2b^{2} = 0, `x=a/b`, `x=b/a`

#### Solution

We have been given that,

a^{2}x^{2} - 3abx + 2b^{2} = 0, `x=a/b`, `x=b/a`

Now if `x=a/b` is a solution of the equation then it should satisfy the equation.

So, substituting `x=a/b` in the equation, we get

a^{2}x^{2} - 3abx + 2b^{2}

`=a^2(a/b)^2-3ab(a/b)+2b^2`

`=(a^4-3a^2b^2+2b^4)/b^2`

Hence `x=a/b` is not a solution of the quadratic equation.

Also, if `x=b/a` is a solution of the equation then it should satisfy the equation.

So, substituting `x=b/a` in the equation, we get

a^{2}x^{2} - 3abx + 2b^{2}

`=a^2(b/a)^2-3ab(b/a)+2b^2`

= b^{2} - 3b^{2} + 2b^{2}

= 0

Hence `x=b/a` is a solution of the quadratic equation.

Therefore, from the above results we find out that `x=a/b` is not a solution and `x=b/a` is a solution of the given quadratic equation.