Question

if x= 7+4 root 3 find the value of x + 1/x

Answer 1

Hey mate!

Here's ur answer dear:)
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$x = 7 + 4 \sqrt{3} \\ \frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{(7) {}^{2} - (4 \sqrt{3}) {}^{2} } \\ \\ \frac{1}{x} = \frac{7 - 4 \sqrt{3} }{49 - 48} = 7 - 4 \sqrt{3}$

Now,

$x + \frac{1}{x} = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \\ \\ x + \frac{1}{x} = 7 + 7 \\ \\ x + \frac{1}{x} = 14$

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HOPE IT HELPS!

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