Question

4x^-4ax+a^-b^ do it by quadratic equation

Answer 1

Hey

Constant term:
a^2- b^2=(a+b)(a-b)

Expression of middle term with relation to constant term:

-4ax= -2[(a+b)+(a-b)]


$4x {}^{2} - 4ax + a {}^{2} - b {}^{2} = 0 \\ \\ = > 4x {}^{2} - 4ax + (a + b)(a - b) = 0 \\ \\ = > 4x {}^{2} - 2 \: ((a + b) + (a - b))x + (a + b)(a - b) = 0 \\ \\ = > 4x {}^{2} - 2x(a + b) - 2x(a - b) + (a + b)(a - b) = 0 \\ \\ = > 2x(2x - (a + b)) - (a - b)(2x - (a + b)) = 0 \\ \\ = > (2x - (a + b))(2x - (a - b)) = 0 \\ \\ = > x = \frac{a + b}{2} \: \: or \: \: \frac{a - b}{2}$

I hope it helps you!!