Question

if `x =  (sqrt3 + 1)/2` find the value of `4x^2 +2x^2 - 8x + 7` 

Answer 1

We have `x = (sqrt3 + 1)/2`

It can be simplified as

`2x - 1 = sqrt3`

On squaring both sides, we get 

`(2x - 1)^2 = (sqrt3)^2`

`(2x)^2 + 1 - 2 xx 2x = 3`

`4x^2 + 1 - 4x = 3`

`4x^2 - 4x - 2 = 0`

The given equation can be rewritten as `4x^2 + 2x^2 - 8x + 7 = x(4x^2 - 4x - 2) + 3 + 7`

Therefore, we have 

`4x^3 + 2x^2 - 8x + 7 = x(0) + 6/4 (0) + 3 + 4`

= 3  + 7

= 10

Hence, the value of given expression is 10