Question

solve by using quadratic formula method x square - 2 aX +( a + 1)(a - 1)​

Answer 1

$\huge\color{red}\boxed{Answer}$

$\color{indigo}\boxed{x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a} }$

where a = 1 b= -2a c = (a+b)(a+b)

by simplification

x²-2ax + a² - b²

by putting value in formula

$x = \frac{ - ( - 2a)± \sqrt{ { - 2a}^{2} - 4(1) {a}^{2} - {b}^{2} } }{2)1(}$

$x = \frac{2a± \sqrt{ 4 {a}^{2} - 4 {a}^{2} - 4 {b}^{2} } }{2}$

$x = \frac{2a± \sqrt{ - 4 {b}^{2} } }{2a}$

Frome here two cases are possible

1st case

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

2nd case

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

$\huge\color{green}\boxed{explanation}$

• here we apply quadratic formula to find value of x in given equation

• then as we can see we reduce equation further

• as we can see c = (a-b)(a+b) which = a² -b² property

• then we put value in equation and get two conditions

• solve both of them and get answer

• you could also solve this equation by factorising the mid term

hope it helps you

be brainly