Question

Page : 1.5
If $x = \frac{\sqrt{3}+1}{2}$ , then value of 4x³ + 2x² - 8x + 7 is :
a) 10
b) 17
c) 21
d) 132

Answer 1

Heya friend,
Here is it,

4(√3 + 1/2)^3 + 2(√3 + 1/2)^2 - 8(√3 + 1/2) +7

= 4(√3 + 1)^3/8 + 2(√3 + 1)^2/4
- 8(√3 + 1)/2 + 7

= (√3 + 1)^3/2 + (√3 + 1)^2/2 - 4(√3 + 1) + 7

As we know,
(a+b)^3 = a^3 + b^3 + 3a^2b + 3 ab^2
And
(a+b)^2 = a^2 + b^2 + 2ab
We get,

[ (√3)^3 + (1)^3 + 3*(√3)^2*1 + 3*√3*(1)^2 ] / 2 + [ (√3)^2 + 2*√3*1 + (1)^2] / 2 - 4(√3 + 1) + 7

= (3√3 + 1 + 9 + 3√3) / 2 + ( 3 + 2√3 + 1) / 2 - 4√3 - 4 + 7

= 6√3 + 10 / 2 + 4 + 2√3 / 2 - 4√3 + 3

By taking 2 common in first two and the by canceling further, we get,

= 3√3 + 5 + 2 + √3 - 4√3 + 3

= 4√3 + 7 - 4√3 +3

= 10




Thank you
Plz mark it as brainiliest
I have worked very hard
@manav
:)

Answer 2

I hope it will help you .