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Question
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
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