Question

If underoot7+4 root 3=x the x+1/x is what

Answer 1

Hey friend,
Here is the answer you were looking for:
$x = \sqrt{7} + 4 \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{7} + 4 \sqrt{3} } \\ \\ on \: rationalizing \: the \: denominator \: we \: get \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{7} + 4 \sqrt{3} } \times \frac{ \sqrt{7} - 4 \sqrt{3} }{ \sqrt{7} - 4 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{1}{x} = \frac{ \sqrt{7} - 4 \sqrt{3} }{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } \\ \\ \frac{1}{x} = \frac{ \sqrt{7} - 4 \sqrt{3} }{49 - 48} \\ \\ \frac{1}{x} = \sqrt{7} - 4 \sqrt{3} \\ \\ x + \frac{1}{x} = ( \sqrt{7} + 4 \sqrt{3} ) + ( \sqrt{7} - 4 \sqrt{3} ) \\ \\ x + \frac{1}{x} = \sqrt{7} + 4 \sqrt{3} + \sqrt{7} - 4 \sqrt{3} \\ \\ x + \frac{1}{x} = \sqrt{7} + \sqrt{7} \\ \\ x + \frac{1}{x} = 2 \sqrt{7}$


Hope this helps!!!

@Mahak24

Thanks...
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