If-x-1-x-9-find the value of-x4-1-x4-

X+1/x=9 Squaring on both sides, (x+1/x )^2=(9)^2 x^2+1/x^2+2× x×1/x=81 ⇒ x^2+1/x^2+2=81 ⇒ x^2+1/x^2=81 2=79 Again squaring on both sides, (x^2+1/x^2 )^2=(79)^2 ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities

If x+1/x=9, f...

Question

$I f x + \frac{1}{x} = 9, find the value of x^{4} + \frac{1}{x^{4}} .$

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Solution

$x + \frac{1}{x} = 9 Squaring on both sides, {(x + \frac{1}{x})}^{2} = (9)^{2} x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x} = 81 \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 81 \Rightarrow x^{2} + \frac{1}{x^{2}} = 81 - 2 = 79 Again squaring on both sides, {(x^{2} + \frac{1}{x^{2}})}^{2} = (79)^{2} \Rightarrow (x^{2})^{2} + {(\frac{1}{x^{2}})}^{2} + 2 \times x^{2} \times \frac{1}{x^{2}} = 6241 \Rightarrow x^{4} + \frac{1}{x^{4}} + 2 = 6241 \Rightarrow x^{4} + \frac{1}{x^{4}} = 6241 - 2 = 6239 ∴ x^{4} + \frac{1}{x^{4}} = 6239$

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If x+1x=9, find the value of x4+1x4.

x+1x=9Squaring on both sides,(x+1x)2=(9)2x2+1x2+2×x×1x=81⇒ x2+1x2+2=81⇒ x2+1x2=81−2=79Again squaring on both sides,(x2+1x2)2=(79)2⇒ (x2)2+(1x2)2+2×x2×1x2=6241⇒ x4+1x4+2=6241⇒ x4+1x4=6241−2=6239∴ x4+1x4=6239

$I f x + \frac{1}{x} = 9, find the value of x^{4} + \frac{1}{x^{4}} .$