Question

if x = √13+2√3find the value of x-1byx

Answer 1

hope it will help you !

Answer 2

Hey friend,
Here is the answer you were looking for:
$x = \sqrt{13} + 2 \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{13} + 2 \sqrt{3} } \\ \\ on \: rationalizing \: the \: denminator \: we \: get \\ \\ \frac{1}{x} = \frac{1}{ \sqrt{13} + 2 \sqrt{3} } \times \frac{ \sqrt{13} - 2 \sqrt{3} }{ \sqrt{13} - 2 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ = \frac{ \sqrt{13} - 2 \sqrt{3} }{ {( \sqrt{13}) }^{2} - {(2 \sqrt{3}) }^{2} } \\ \\ = \frac{ \sqrt{13} - 2 \sqrt{3} }{13 - 12} \\ \\ \frac{1}{x} = \sqrt{13} - 2 \sqrt{3} \\ \\ x - \frac{1}{x} = ( \sqrt{13} + 2 \sqrt{3} ) - ( \sqrt{13} - 2 \sqrt{3} ) \\ \\ x - \frac{1}{x} = \sqrt{13} + 2 \sqrt{3} - \sqrt{13} + 2 \sqrt{3} \\ \\ x - \frac{1}{x} = 2 \sqrt{3} + 2 \sqrt{3} \\ \\ x - \frac{1}{x} = 4 \sqrt{3}$


Hope this helps!!!!

@Mahak24

Thanks...
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