Question

HOLA,




$\huge \fbox \red{❥ Question}$



Solve the following quadratic equation for x: x2 – 2ax – (4b2 – a2) = 0) ​

Answer 1

$\sf \Large Solution!!$

$\sf x^{2}-2ax-(4b^{2}-a^{2})=0$

$\sf \large Comparing\:with:$

$\sf ax^{2}+bx+c=0$

$\sf \large We\:get:$

$\sf \to a=1$

$\sf \to b=-2a$

$\sf \to c=-4b^{2}+a^{2}$

$\sf \large Now,$

$\sf \to x=\dfrac{-b±\sqrt{b^{2}-4ac}}{2a}$

$\sf \to x=\dfrac{-(-2a)±\sqrt{(-2a)^{2}-4\times 1\times (-4b^{2}+a^{2})}}{2\times 1}$

$\sf \to x=\dfrac{2a±\sqrt{\cancel{4a^{2}}+16b^{2}\cancel{-4a^{2}}}}{2}$

$\sf \to x=\dfrac{2a±\sqrt{16b^{2}}}{2}$

$\sf \to x=\dfrac{2a±4b}{2}$

$\sf \to x=\dfrac{\cancel 2(a±2b)}{\cancel 2}$

$\sf \to x=a±2b$

$\sf \boxed{\bigstar x=a+2b\:or\:x=a-2b}$

Thanks for asking!! :)

Answer 2

Answer:

Hopes the attachment helps you ✌