InterviewSolution
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InterviewSolution
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If x² + 1/x² = 27, find x² - 1/x² |
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Answer» –• x² + 1/x² = 27TO FIND :–• Value of x² - 1/x² = ?SOLUTION :–• We know that –➪ (a+b)² = a² + b² + 2ab⇒ (x + 1/x)² = x² + 1/x² + 2(x)(1/x)⇒ (x + 1/x)² = 27 + 2⇒ (x + 1/x)² = 29⇒ x + 1/x = √29 _____________eq.(1)• We ALSO know that –➪ (a-b)² = a² + b² - 2ab⇒ (x - 1/x)² = x² + 1/x² - 2(x)(1/x)⇒ (x - 1/x)² = 27 - 2⇒ (x - 1/x)² = 25⇒ x - 1/x = √25⇒ x - 1/x = ±5 _____________eq.(2)• One more identity to use –➪ (a-b)(a+b) = a² - b²• Now MULTIPLY EQ.(1) & eq.(2) –⇒ (x + 1/x)(x - 1/x) = ±5(√29)⇒ x² - 1/x² = ±5√29 ▪︎ HENCE , The Value of x² - 1/x² is ±5√29. |
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