Question

If x + 1x =7, Evaluate x2 + 1 x2\

Answer 1

Correct Question:

$\boxed{ \text{If } x+\dfrac{1}{x} = 7, \text{ then find the value of: } x^2 + \dfrac{1}{x^2} }$

Answer:

Given:

$\implies \bf{ x+\dfrac{1}{x} = 7 }$

Squaring on both sides we get:

$\implies ( x + \dfrac{1}{x} )^2 = (7)^2\\\\\\\implies ( x^2 + 2 \times x \times \dfrac{1}{x} + \dfrac{1}{x^2} ) = 49\\\\\\\implies ( x^2 + 2 \times \dfrac{x}{x} + \dfrac{1}{x^2}) = 49\\\\\\\implies ( x^2 + 2 (1) \times \dfrac{1}{x^2} ) = 49\\\\\\\text{Transposing 2 to the RHS, we get: }\\\\\\\implies x^2 + \dfrac{1}{x^2} = 49 - 2\\\\\\\implies \boxed{ \bf{ x^2 + \dfrac{1}{x^2} = 47 }}$

Hence the required value is 47.

Answer 2

Step-by-step explanation:

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