Question

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

How do I solve this ?

Answer 1

Explanation:

(x + a)(x - b) = x² - 1

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

By equality :

a = 1

b ÷ -1

Answer 2

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.

`</p><p>x+1=0\Rightarrow\boxed{x_1=-1} \\</p><p>x-1=0\Rightarrow\boxed{x_2=1}</p><p>`

Hope this helps.