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If (x+1/x)=4, find the value of (x²+1/x²) |
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Answer» Answer: x 2 + x 2
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=14 Step-by-step explanation: We have, x+\dfrac{1}{x}=4x+ x 1
=4 .....(1) To find, x^2+\dfrac{1}{x^2}=?x 2 + x 2
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=? Squaring (1) in both SIDES, we GET (x+\dfrac{1}{x})^{2}=4^{2}(x+ x 1
) 2 =4 2
⇒ x^2+\dfrac{1}{x^2}+2.x.\dfrac{1}{x} =16x 2 + x 2
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+2.x. x 1
=16 ⇒ x^2+\dfrac{1}{x^2}+2 =16x 2 + x 2
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+2=16 ⇒x^2+\dfrac{1}{x^2}=16-2=14x 2 + x 2
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=16−2=14 ∴ x^2+\dfrac{1}{x^2}=14x 2 + x 2
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=14 Hence, x^2+\dfrac{1}{x^2}=14x 2 + x 2
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=14 |
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