1.

Solve the following quatratic equation : `4x^(2)-2(a^(2)+b^(2))x+a^(2)b^(2)=0`

Answer» 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.


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