If value of x+1/x is 3+√8 …

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If value of x+1/x is 3+√8 than find the value of x^2+1/x^2

Posted by Sneh Lata Kamal 5 years, 9 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 9 months ago

It is given that,
x = 3 + $\sqrt{8}$
Now, $\frac{1}{x}$ = $\frac{1}{3+\sqrt{8}}$ = $\frac{1}{3+\sqrt{8}} \times \frac{3-\sqrt{8}}{3-\sqrt{8}}$ ( rationalising the expression)
= $\frac{3-\sqrt{8}}{(3)^{2}-(\sqrt{8})^{2}}$
= $\frac{3-\sqrt{8}}{9-8}$ = 3 - $\sqrt{8}$
$\Rightarrow$ $\frac{1}{x}$ = 3 - $\sqrt{8}$
We know that, (x + $\frac{1}{x}$ )² = x² + $\frac{1}{x^2}$ + 2 $\times$ x $\times$ $\frac{1}{x}$
$\Rightarrow$ (3 + $\sqrt{8}$ + 3 - $\sqrt{8}$ )² = x² + $\frac{1}{x^2}$ + 2
$\Rightarrow$ (6)² = x² + $\frac{1}{x^2}$ + 2
$\Rightarrow$ 36 = x² + $\frac{1}{x^2}$ + 2
$\Rightarrow$ x² + $\frac{1}{x^2}$ = 36 - 2 = 34
Hence, x² + $\frac{1}{x^2}$ = 34

1Thank You

ANSWER

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CBSE > Class 09 > Mathematics