if [x+1/x]=12, find the value of [x²+1/x²]
Answers
Answered by
4
EXPLANATION.
⇒ (x + 1/x) = 12.
As we know that,
Squaring on both sides of the equation, we get.
⇒ (x + 1/x)² = (12)².
⇒ (x)² + (1/x)² + 2(x)(1/x) = 144.
⇒ x² + 1/x² + 2 = 144.
⇒ x² + 1/x² = 144 - 2.
⇒ x² + 1/x² = 142.
Answered by
5
x² + (1/x)² = 142
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Explanation :
x + (1/x) = 12 ____(Given in Question)
so , Squaring on both sides
⇒ [x + (1/x)]² = (12)²
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by using ,
(x + y)² = x² + y² + 2xy
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so ,
⇒ x² + (1/x)² + 2x(1/x) = 144
⇒ x² + (1/x)² = 144 - 2 = 142
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Final Answer :
x² + (1/x)² = 142
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