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Question

If x+x​​​​​​-1 = 11, Then x​​​​​​2+x​​​​​​2 = ?


Solution

Given x - 1/x = 11
squaring on both sides we get

⇒ (x-1/x)2=112

⇒ x2+1/x2-2(x)(1/x)=121......(a-b)2=a2+b2-2ab

⇒ x2+1/x2-2=121

⇒ x2+1/x2 = 121+2 = 123

∴ x2+1/x2=123

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