If x - 9-4-5- find the value of x2-1-x2

X=9 4√(5) nbsp; nbsp; [Given] Taking reciprocal. 1/x=1/9 4√(5) 1/x = [1 × (9+4√(5))] / [(9 4√(5)) × (9+4√(5))] 1/x=9+4√(5)/(81 80) 1/x=9+4√(5) (1.5 ...

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Byju's Answer

Standard IX

Mathematics

Expansion of (a ± b ± c)²

If x = 9-4√5,...

Question

If x = 9-4 $\sqrt{5}$ , find the value of $x^{2} + \frac{1}{x^{2}}$

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Solution

$x = 9 - 4 \sqrt{5} [G i v e n] T a k i n g r e c i p r o c a l . \frac{1}{x} = \frac{1}{9 - 4 \sqrt{5}} \frac{1}{x} = \frac{[1 \times (9 + 4 \sqrt{5})]}{[(9 - 4 \sqrt{5}) \times (9 + 4 \sqrt{5})]} \frac{1}{x} = \frac{9 + 4 \sqrt{5}}{(81 - 80)} \frac{1}{x} = 9 + 4 \sqrt{5} (1.5 M a r k s) A . T . Q x^{2} + \frac{1}{x^{2}} = (9 - 4 \sqrt{5})^{2} + (9 + 4 \sqrt{5})^{2} = [9^{2} + (4 \sqrt{5})^{2} - 2 \times 9 \times 4 \sqrt{5}] + [9^{2} + (4 \sqrt{5})^{2} + 2 \times 9 \times 4 \sqrt{5}) = [81 + 80 - 72 \sqrt{5}] + [81 + 80 + 72 \sqrt{5}] = 161 - 72 \sqrt{5} + 161 + 72 \sqrt{5} = 322 (1.5 M a r k s)$

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Similar questions

Q. If

x = 9 + 4 \sqrt{5}

, find the value of

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

Q. If

x = 9 - 4 \sqrt{5},

then find the value of

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

Q. If x = 9-4

\sqrt{5}

, find the value of

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

Q. If

x + \frac{1}{x} = 9

and

x^{2} + \frac{1}{x^{2}} = 5

. Find the value of

x - \frac{1}{x}

If x =9-4√5 , find x² +1/x²

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If x = 9-4√5, find the value of x2+1x2

x=9−4√5 [Given] Taking reciprocal. 1x=19−4√51x=[1×(9+4√5)][(9−4√5)×(9+4√5)]1x=9+4√5(81−80)1x=9+4√5 (1.5 Marks)A.T.Qx2+1x2=(9−4√5)2+(9+4√5)2=[92+(4√5)2−2×9×4√5]+[92+(4√5)2+2×9×4√5)=[81+80−72√5]+[81+80+72√5]=161−72√5+161+72√5=322 (1.5 Marks)

If x = 9-4 $\sqrt{5}$ , find the value of $x^{2} + \frac{1}{x^{2}}$