Question

$if x + \frac{1}{x} = 3 \: \: find \: \: x ^{2} + \frac{1}{x ^{2} }$
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Answer 1

Answer : 7

Step - by - step Explanation :

x + 1/x = 3

Squaring on both sides we get,

(x² + 1/x)² = (3)²

(x + 1/x)² = 9

We know that,

(a + b)² = a² + 2ab + b²

Use the above formula in the problem.

x² + 2(x)(1/x) + (1/x)² = 9

x² + 2x/x + 1/x² = 9

x² + 2 + 1/x² = 9

Transport 2 into RHS

x² + 1/x² = 9 - 2

x² + 1/x² = 7

Therefore, x² + 1/x² = 7