# If X = (Sqrt3 + 1)/2 Find the Value of 4x^2 +2x^2 - 8x + 7 - Mathematics

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

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#### Solution

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

Concept: Operations on Real Numbers
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#### APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 3 Rationalisation
Exercise 3.2 | Q 12 | Page 15

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