Question

(x+1/x)^2=96.whats the value of x^2+1/x^2​

Answer 1

Answer:

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Step-by-step explanation:

$(x + \frac{1}{x}) {}^{2} = 96 \\ so \: \: \:( x + \frac{1}{x}) = 4 \sqrt{6}$

$x {}^{2} + \frac{1}{x {}^{2} } = (x + \frac{1}{x}) {}^{2} - 2 \times x \times \frac{1}{x} \\ = (4 \sqrt{6}) {}^{2} - 2 \\ = 16 \times 6 - 2 \\ = 96 - 2 \\ = 94$

Answer 2

The correct answer is "94". Further explanation is given below.

Step-by-step explanation:

If, given:

$(x+\frac{1}{x})^2 = 96$

then,

$(x+\frac{1}{x}) = \sqrt[4]{6}$

As we know,

$(x+\frac{1}{x})^2=x^2+\frac{1}{x^2}+2*x*\frac{1}{x}$

∵ (a+b)² = a²+b²+2ab

Now,

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

On putting the values in the above equation, we get

⇒  $(\sqrt[4]{6})^2-2$

⇒  16×6-2

⇒  96-2

⇒  94

Hence the value of  $x^2+\frac{1}{x^2} = 94$.

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