Question

PLEASE solve this maths question FAST AND URGENT I LL MARK AS BRAINIEST PLEASE ANSWER IN NB WITH STEPS PLEASE

Answer 1

Given Equation is x^4 - 4abx^2 - (a^2 - b^2)^2.

Let x^2 = d.

here, a = 1, b = -4ab, c = -(a^2 - b^2)^2

(1)

$=>x = \frac{-b + \sqrt{b^2 - 4ac} }{2a}$

$=> \frac{-(-4ab) + \sqrt{16a^2b^2 + 4(a^2 - b^2)^2}}{2}$

$=> 2ab+\sqrt{4a^2b^2 + (a^2 - b^2)^2}$

$=> 2ab + \sqrt{4a^2b^2 + a^4 + b^4 - 2a^2b^2}$

$=> 2ab + \sqrt{a^4 + b^4 + 2a^2b^2}$

$=> 2ab + \sqrt{(a^2 + b^2)^2}$

$=> 2ab + a^2 + b^2$

So, d = 2ab + a^2 + b^2

= > d = (a + b)^2

= > x^2 - (a + b)^2

= > x - (a + b), x + (a + b)

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(ii)

$=> d = \frac{4ab - \sqrt{16a^2b^2 + 4(a^2 - b^2)} }{2}$

$=> d = 2ab - \sqrt{(a^2 - b^2)^2}$

$=> d = 2ab - (a - b)^2$

$=> x^2 + (a - b)^2$

Therefore, x^2 + (a + b)^2 is not a factor of x^4 - 4abx^2 - (a^2 - b^2)^2.

Hope this helps!