Question

solve for x: (x+a)(x-b) = x^2 -1

How do I solve this ?

Answer 1

You must factor.

$x^2-1=(x+1)(x-1)$

The factored form is equal to the assigned form.

$(x+1)(x-1)=(x+a)(x-b)$

Values a, b correspond to the factored 1, -1.

Value of x however remains unknown. But we can change that.

Given factored result,

$(x+1)(x-1)$

We can set expression equal to 0 then find such x that when added with number a or b results with 0.

$(x+1)(x-1)=0$

Hence x has 2 solutions.

$

x+1=0\Rightarrow\boxed{x_1=-1} \\

x-1=0\Rightarrow\boxed{x_2=1}

$

Hope this helps.

Answer 2

Step-by-step explanation:

(x + a)(x - b) = x² - 1

(x + a)(x - b) = (x + 1)(x - 1)

By equality :

a = 1

b ÷ -1