Question

given, 1/x +x=2 find value of 1/x^2 +x^2​

Answer 1

Answer:

$x + \frac{1}{x} = 2 \\ \\ \\ = > \frac{1}{ {x}^{2} } + {x}^{2} = \\ \\ \\ = > (x + \frac{1}{x} )^{2} - 2 = {2}^{2} \\ \\ \\ = >( x + \frac{1}{x} ) {}^{2} = 4 + 2 \\ \\ \\ = >( x + \frac{1}{x} ) {}^{2} = 6 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 6 \\ \\ = > {x}^{2} + \frac{1}{ {x}^{2} } = 6 - 2 \\ \\ \\ = > > {x}^{2} + \frac{1}{ {x}^{2} } = 4$

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Answer 2

Answer:

1/x² + x² = 2

Step-by-step explanation:

Given

1/x + x = 2

1/x² + x² = ?

(1/x + x)² = 2² = 4

⇒ x² + 1/x² + 2 × x × 1/x = 4

⇒ x² + 1/x² + 2 = 4

x² + 1/x² = 4-2 = 2

∴ 1/x² + x² = 2