Solve the following quadratic equations by factorization method: `4x^2-2(a^2+b^2)x+a^2b^2=0` `9x^2-9(a+b)x+(2x^2+5a b+2b^2)=0`

Explanation

Given equation is
`4x^(2)-2(a^(2)+b^(2))x+a^(2)b^(2)=0`
`implies4x^(2)-2a^(2)x-2b^(2)x+a^(2)b^(2)=0`
`implies2x(2x-a^(2))-b^(2)(2x-a^(2))=0`
`implies(2x-a^(2))(2x-b^(2))=0`
`implies2x-a^(2)=0or2x-b^(2)=0`
when `2x-a^(2)=0impliesx=(a^(2))/(2)`
and `2x-b^(2)=0impliesx=(b^(2))/(2)`
Hence, `a^(2)/(2)and(b^(2))/(2)` are roots of the equation.