Find the value of x2-1-x2 when x-32 -2

Given: x=32√(2) (x+1/x)^2 = x^2+1/x^2+2× x×1/x (x+1/x)^2 =(32√(2))^2+1/(32√(2))^2+2× (32√(2))×1/(32√(2)) =2048+ 1/2048 + 2 = 2028+0.00048 = 2048.00048 ...

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Standard X

Mathematics

Addition of Rational Expressions

Find the valu...

Question

Find the value of $x^{2} + \frac{1}{x^{2}}$ when $x = 32 \sqrt{2}$

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Solution

Given: $x = 32 \sqrt{2}$
$(x + \frac{1}{x})^{2}$ = $x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x}$
$(x + \frac{1}{x})^{2}$ = $(32 \sqrt{2})^{2} + \frac{1}{(32 \sqrt{2})^{2}} + 2 \times (32 \sqrt{2}) \times \frac{1}{(32 \sqrt{2})}$
= $2048 + \frac{1}{2048} + 2$

= 2028+0.00048
= 2048.00048

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Find the value of x2+1x2 when x=32√2

Given: x=32√2 (x+1x)2 = x2+1x2+2×x×1x (x+1x)2 =(32√2)2+1(32√2)2+2×(32√2)×1(32√2) =2048+12048+2 = 2028+0.00048 = 2048.00048

Find the value of $x^{2} + \frac{1}{x^{2}}$ when $x = 32 \sqrt{2}$

Given: $x = 32 \sqrt{2}$
$(x + \frac{1}{x})^{2}$ = $x^{2} + \frac{1}{x^{2}} + 2 \times x \times \frac{1}{x}$
$(x + \frac{1}{x})^{2}$ = $(32 \sqrt{2})^{2} + \frac{1}{(32 \sqrt{2})^{2}} + 2 \times (32 \sqrt{2}) \times \frac{1}{(32 \sqrt{2})}$
= $2048 + \frac{1}{2048} + 2$

= 2028+0.00048
= 2048.00048