Question

If x² + 1/x² = 79, find the value of x + 1/x

Answer 1

Given :  x² + 1/x² = 79

We know that, (x + 1/x)² = x² + (1/x)² + 2 × x × 1/x  

[By using identity , (a + b)²  = a² + b² + 2ab]

(x + 1/x)² = x² + (1/x)² + 2  

(x + 1/x)² = 79 + 2

(x + 1/x)² = 81

(x + 1/x) = ± √81

[Taking square root on both sides]

x + 1/x = ± 9

Hence the value of x + 1/x is ± 9.  

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