Question

Find the roots of the following quadratic equation by the factorization method :

4x2 − 4ax + (a2 − b2) = 0​

Answer 1

Step-by-step explanation:

Thank me ✌✌✌✌✌☕☕-☺☺☺-

Answer 2

$\mathtt{\huge{\underline{\red{Question\:?}}}}$

✴ Find the roots of the following quadratic equation by the factorization method :

4x² − 4ax + (a² − b²) = 0

$\mathtt{\huge{\underline{\green{Answer:-}}}}$

✒ $x = \dfrac{a + b}{2}$ , $x = \dfrac{a - b}{2}$

$\mathtt{\huge{\underline{\orange{Solution:-}}}}$

Given :-

• A quadratic equation :- 4x² − 4ax + (a² − b²) = 0.

To Find :-

• The roots of the following quadratic equation by the factorization method.

Calculation :-

According to the question,

A quadratic equation is 4x² - 4ax + (a²-b²) =0

4x² - 4ax + (a²-b²) =0

We know that, (a²-b²) = (a+b) (a-b)

➡ 4x² - 4ax + (a+b) (a-b) =0

➡ 4x²+[-2a - 2a +2b - 2b]x + (a - b)(a + b) = 0

➡ 4x²+ (2b - 2a) x - (2a +2b)x + (a-b)(a +b) =0

➡ 4x²+2(b-a)x - 2(a +b) x +(a- b) (a + b)= 0

➡ 2x- [2x - (a-b)] - (a +b)[2x - (a -b)] =0

➡ 2x (a - b) = 0, 2x - (a +b) = 0

Firstly,

2x (a - b) = 0

=> $x = \dfrac{a + b}{2}$

Secondly,

2x - (a +b) = 0

=> $x = \dfrac{a - b}{2}$

______________________________________