Question

Find the values if a and b such that x squared + 2x -7 = (x+a) squared + b​

Answer 1

Given:

`x^2+2x-7=(x+a)^2+b`

To find:

The values of a and b.

Solution:

We have,

`x^2+2x-7=(x+a)^2+b`

It can be written as

`(x^2+2x)-7=(x+a)^2+b`

Add and subtract square of half of coefficient of x in the parenthesis.

`(x^2+2x+((2)/(2))^2-((2)/(2))^2)-7=(x+a)^2+b`

`(x^2+2x+1^2)-1-7=(x+a)^2+b`

`(x+1)^2-8=(x+a)^2+b`
`[\because (x+y)^2=x^2+2xy+y^2]`

`(x+1)^2+(-8)=(x+a)^2+b`

On comparing both sides, we get

`a=1`

`b=-8`

Therefore, the value of a is 1 and the value of b is -8.