Question

Solve for x:

4x² + 4bx − (a² − b²) = 0

Answer 1

The given quadratic equation is.`4x^2+4bx-(a^2-b^2)=0`

`4x^2+2(a+b)x-2(a-b)x-(a^2-b^2)=0`

`2x(2x+a+b)-(a-b)(2x+a+b)=0`

Therefore,

`2x-(a-b)=0`

`2x=a-b`

`x=(a-b)/2`

or

`2x+a+b=0`

`2x=a-b`

`x=(a-b)/2`

or

`2x+a+b=0`

`2x=-(a+b)`

`x=-(a-b)/2`

Thus, the solutions of the given quadratic equation are

\[\left( \frac{a - b}{2} \right)\]and\[- \left( \frac{a + b}{2} \right) .\]