Question

Find the value of n such that x2 – 11x + n is a perfect square trinomial.

Answer 1

n = 121/4

(x - 11/2)^2
x^2 - 11x + 121/4

Answer 2

`n=(121)/(4)`

Explanation:

Given:
`x^2-11x+n`

The given expression is perfect square trinomial.

The middle term is negative.

`a^2-2ab+b^2=(a-b)^2`

`\Rightarrow x^2-11x+n`

`\Rightarrow x^2-11x+n=a^2-2ab+b^2`

Compare both sides

`a=x`

`2ab=11x`

`b^2=n`

Using three equation to solve for n

`2xb=11x`
`\because a=x`

`b=(11)/(2)`

Now, we will put b

`n=b^2`

`n=((11)/(2))^2`

`n=(121)/(4)`

Hence, The value of n is 121/4 which makes perfect square trinomial.