If `x=(sqrt(3)+1)/2,` find the value of `4x^3+2x^2-8x+7.`

Explanation

To find the value of the expression \(4x^3 + 2x^2 - 8x + 7\) given \(x = \frac{\sqrt{3} + 1}{2}\), we will substitute the value of \(x\) into the expression and simplify step by step.

### Step 1: Substitute \(x\) into the expression
We start with the expression:
\[ 4x^3 + 2x^2 - 8x + 7 \]
Substituting \(x = \frac{\sqrt{3} + 1}{2}\):
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