X-1-x-3-then-x6-1-x6-364927414322

The correct option is D 322 x+1/x=3 Squaring, we get x^2+1/x^2+2=9 ⇒ x^2+1/x^2=9 2=7 Cubing both sides, (x^2+1/x^2 )^3=(7)^3 x^6+1/x^6+3(x^2+1/x^2 )=343 ⇒ x^ ...

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Byju's Answer

Standard IX

Mathematics

Algebraic Identities

x+1/x=3 then ...

Question

$x + \frac{1}{x} = 3 t h e n x^{6} + \frac{1}{x^{6}} =$

927

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414

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364

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322

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Solution

The correct option is D
322

$x + \frac{1}{x} = 3 Squaring, we get x^{2} + \frac{1}{x^{2}} + 2 = 9 \Rightarrow x^{2} + \frac{1}{x^{2}} = 9 - 2 = 7 Cubing both sides, {(x^{2} + \frac{1}{x^{2}})}^{3} = (7)^{3} x^{6} + \frac{1}{x^{6}} + 3 (x^{2} + \frac{1}{x^{2}}) = 343 \Rightarrow x^{6} + \frac{1}{x^{6}} + 3 \times 7 = 343 \Rightarrow x^{6} + \frac{1}{x^{6}} + 21 = 343 \Rightarrow x^{6} + \frac{1}{x^{6}} = 343 - 21 = 322$

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Similar questions

Q. If

x + \frac{1}{x} = 3

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x+1x=3 then x6+1x6=

The correct option is D 322 x+1x=3Squaring, we getx2+1x2+2=9⇒ x2+1x2=9−2=7Cubing both sides,(x2+1x2)3=(7)3x6+1x6+3(x2+1x2)=343⇒ x6+1x6+3×7=343⇒ x6+1x6+21=343⇒ x6+1x6=343−21=322

$x + \frac{1}{x} = 3 t h e n x^{6} + \frac{1}{x^{6}} =$