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If x +1/x =sqrt6, find the value of x^2+1/2

Answer»

CORRECT question: If x + 1/x = √6, FIND the value of x² + 1/x².

Answer:

\boxed{ \bf \therefore \: {x}^{2} + \frac{1}{x {}^{2} } = 4}

Step-by-step EXPLANATION:

GIVEN that ;

\implies \sf x + \frac{1}{x} = \sqrt{6} \\ \\ \bf On \: squaring \: both \: sides : \\ \\ \implies \sf (x + \frac{1}{x} ) {}^{2} = ( \sqrt{6} ) {}^{2} \\ \\ \implies \sf {x}^{2} + \frac{1}{x {}^{2} } + 2 \times x \times \frac{1}{x} = 6 \\ \\ \implies \sf {x}^{2} + \frac{1}{x {}^{2} } + 2 = 6 \\ \\ \implies \sf {x}^{2} + \frac{1}{x {}^{2} } = 6 - 2 \\ \\ \boxed{ \bf \therefore \: {x}^{2} + \frac{1}{x {}^{2} } = 4}


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