If x=1/2times root 7, then find the value of x^2-x/2 times root 7+1

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Solution

$x = \frac{\sqrt{7}}{2} Now, x^{2} - \frac{x}{2} \sqrt{7} + 1 = {(\frac{\sqrt{7}}{2})}^{2} - \frac{\sqrt{7}}{2} \times \frac{\sqrt{7}}{2} + 1 = \frac{7}{4} - \frac{7}{2} + 1 = \frac{7 - 14 + 4}{4} = - \frac{3}{4}$

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