If x-2 - -1 - x-2- - 27- find x - 1 - x- - Maths Q - A

Compute the required value.As we know that, (a b)^2=a^2+b^2 2ab.⇒(x 1/x)^2=x^2+1/x^2 2(x×1/x)0ex0ex⇒(x 1/x)^2=27 20ex0ex⇒(x 1/x)^2=25Take square root on both si ...

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

Byju's Answer

Standard X

Mathematics

Rational Expression

If x^2 + (1 /...

Question

If $x^{2} + \frac{1}{x^{2}} = 27$ , find $x - \frac{1}{x}$ .

Open in App

Solution

Compute the required value.
As we know that, ${(a - b)}^{2} = a^{2} + b^{2} - 2 a b$ .
$\Rightarrow {(x - \frac{1}{x})}^{2} = x^{2} + \frac{1}{x^{2}} - 2 (x \times \frac{1}{x}) \Rightarrow {(x - \frac{1}{x})}^{2} = 27 - 2 \Rightarrow {(x - \frac{1}{x})}^{2} = 25$
Take square root on both sides.
$\Rightarrow (x - \frac{1}{x}) = \pm \sqrt{25}$
Hence, the value of $x - \frac{1}{x}$ is $\pm 5$ .

Suggest Corrections

Similar questions

Q. If

α

and

β

are the zeros of the quadratic polynomial

f (x) = x^{2} - x - 2

, find the value of

\frac{1}{α} - \frac{1}{β} .

Q. If

α

and

β

are the roots of the equation

x^{2} - 7 x + 1 = 0

then find the value

\frac{1}{{(α - 7)}^{2}} + \frac{1}{{(β - 7)}^{2}}

Q. If

f (x) = {sin}^{- 1} {\frac{\sqrt{3}}{2} x - \frac{1}{2} \sqrt{1 - x^{2}}}, - \frac{1}{2} \leq x \leq 1,

then

f (x)

is equal to

Q. If

α

and

β

are the zeros of the polynomial

x^{2} + 8 x + 6

, form a quadratic polynomial whose zeros are

\frac{1}{α}

and

\frac{1}{β}

Q. The coefficient of

x^{2}

in the expansion of

\frac{1 + 10 x + x^{2}}{e^{x}}

Join BYJU'S Learning Program

If x2+1x2=27, find x-1x.

Compute the required value.As we know that, a-b2=a2+b2-2ab.⇒x-1x2=x2+1x2-2x×1x⇒x-1x2=27-2⇒x-1x2=25Take square root on both sides.⇒x-1x=±25Hence, the value of x-1x is ±5.

If $x^{2} + \frac{1}{x^{2}} = 27$ , find $x - \frac{1}{x}$ .