Question

Find the root of the following quadratic equation by factorisation method: (a+b)²x²-4abx-(a-b)²=0

Answer 1

We know...
4ab = (a + b) ² - (a - b) ²

Now..
(a +b)²x² - 4abx - (a-b) ²

= (a +b)² x² - {(a+b) ² - (a - b) ²}x - (a - b) ²

= (a+ b) ²x² - (a +b) ²x +(a-b) ²x - (a-b) ²

= (a+b) ²x (x - 1) + (a-b) ²(x-1)

=(x-1){(a+b)²x + (a- b) ²}

= (x - 1) { (a+b) ² x + (a - b) ²}

So... The roots of x are...

X = 1

@nd
$x = - \frac{(a - b)^{2} }{ {(a + b)}^{2} }$
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