X2-1x2-6Find i x3-1x3i x6 -1x6

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 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Componendo and Dividendo

x2+1x2=6Find ...

Question

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

Open in App

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

Suggest Corrections

Similar questions

Q. If x is a proper fraction, show that

\frac{x}{1 - x^{2}} - \frac{x^{3}}{1 - x^{6}} + \frac{x^{5}}{1 - x^{10}} - . . . . . . . = \frac{x}{1 + x^{2}} + \frac{x^{3}}{1 + x^{6}} + \frac{x^{5}}{1 + x^{10}} + . . . . .

Find the coefficient of $x^{15}$ in $(x^{3} + x^{6} + x^{9} + . . . . . . . . . . .) (x^{2} + x^{4} + x^{6} + . . . . . . . . . . .) (x + x^{2} + x^{3} + . . . . . . . . . .)$

Q. Which polynomial is not in standard from?
(i)

x^{3} + x^{2} - 1 = x^{2} + x^{3}

(ii)

(x^{4} + 1) (x - x^{2})

(iii)

x^{6} + x^{3} - x + 1

Q. If

\sqrt{1 - x^{6}} + \sqrt{1 - y^{6}} = a^{3} . (x^{3} - y^{3})

, prove that

\frac{d y}{d x} = \frac{x^{2}}{y^{2}} \sqrt{\frac{1 - y^{6}}{1 - x^{6}}}

Q. The quotient when

1 + x^{2} + x^{4} + x^{6} + \dots + x^{34}

is divided by

1 + x + x^{2} + x^{3} + \dots + x^{17}

Join BYJU'S Learning Program

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) $x^{6} + \frac{1}{x^{6}}$