- x-2-1x-2-6-Find nbsp-i- - x-3-1x-3-i- - x-6 -1x-6-

x ^ 2 + 1 x ^ 2 =6 x ^ 2 + 1 x ^ 2 2=6 2 ( x 1 x #160; ) #160; ^ 2 =4 x 1 x = 2 or 2 Cubing on both sides. x ^ 3 ...

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Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

x^2+1x^2=6 Fi...

Question

$x^{2} + \frac{1}{x^{2}} = 6$
Find
(i) $x^{3} - \frac{1}{x^{3}}$
(i) $x^{6} + \frac{1}{x^{6}}$

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Solution

$x^{2} + \frac{1}{x^{2}} = 6$
$x^{2} + \frac{1}{x^{2}} - 2 = 6 - 2$
${(x - \frac{1}{x})}^{2} = 4$
$x - \frac{1}{x} = 2 o r - 2$
Cubing on both sides.
$x^{3} - \frac{1}{x^{3}} - 3 x . \frac{1}{x} (x - \frac{1}{x}) = 8$
$x^{3} - \frac{1}{x^{3}} = 8 + 3 (x - \frac{1}{x}) = 8 + 6$
$i)$ $x^{3} - \frac{1}{x^{3}} = 14 o r - 14$
Squaring on both sides
$i i)$ $x^{6} - \frac{1}{x^{6}} + 2 = {(14)}^{2} = 196$
$x^{6} - \frac{1}{x^{6}} = 194$ -is the Answer

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x2+1x2=6Find (i) x3−1x3(i) x6+1x6

x2+1x2=6x2+1x2−2=6−2(x−1x)2=4x−1x=2 or −2Cubing on both sides.x3−1x3−3x.1x(x−1x)=8x3−1x3=8+3(x−1x)=8+6i) x3−1x3=14or −14Squaring on both sidesii) x6−1x6+2=(14)2=196x6−1x6=194 -is the Answer

$x^{2} + \frac{1}{x^{2}} = 6$
Find
(i) $x^{3} - \frac{1}{x^{3}}$
(i) $x^{6} + \frac{1}{x^{6}}$