Math, asked by nishavaishnav, 1 year ago

if x=2-√5find x^2+1/x^2

Answers

Answered by AkshithaZayn
2
Hey there!

Given,

x = 2 - \sqrt{5}

Find

x {}^{2} + \frac{1}{x {}^{2} }

(2 - \sqrt{5} ) {}^{2} + \frac{1}{(2 - \sqrt{5} ) {}^{2} }

using expression (a+b)² = a² + 2ab + b²

4 - 4 \sqrt{5} + 5 + \frac{1}{4 - 4 \sqrt{5} + 5 }

4 - 4 \sqrt{5} + 5 + \frac{1}{9 - 4 \sqrt{5} }

Rationalising the denominator

 \frac{1(9 + 4 \sqrt{5}) }{(9 - 4 \sqrt{5}) (9 + 4 \sqrt{5}) }

 \frac{9 + 4 \sqrt{5} }{81 - 80}

9 + 4 \sqrt{5}

4 - 4 \sqrt{5} + 5 + 9 + 4 \sqrt{5}

(cancelling the opposites)

4 + 5 + 9

18

Hope it helps!
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