If x - 1-x - 10 and x - 0- then x-2 nbsp- 1-x-2 - -1029810100

The correct option is B 98Given that, x + 1/x = 10 nbsp;(x + 1/x)^2 =100 Using the identity, (a+b)^2 = a^2+b^2+2ab, we have nbsp;(x + 1/x)^2 = x^2 + 1/ ...

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

Byju's Answer

Standard IX

Mathematics

Algebraic Identity 1

If x + 1/x = ...

Question

If $x + \frac{1}{x} = 10$ and $x \neq 0$ , then $x^{2} + \frac{1}{x^{2}}$ = ___.

102

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

100

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 98
Given that, $x + \frac{1}{x} = 10 ⟹ (x + \frac{1}{x})^{2} = 100$

Using the identity,

$(a + b)^{2} = a^{2} + b^{2} + 2 a b$ , we have

$(x + \frac{1}{x})^{2} = x^{2} + \frac{1}{x^{2}} + 2 (x) (\frac{1}{x})$
$⟹ 100 = x^{2} + \frac{1}{x^{2}} + 2$
$⟹ x^{2} + \frac{1}{x^{2}} = 100 - 2$
$∴ x^{2} + \frac{1}{x^{2}} = 98$

Suggest Corrections

Similar questions

Q. If

x + \frac{1}{x} = 10

and

x \neq 0

, then

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

= ___.

If (x−1/x)=10, then find the value of x²+1/x².

Q. If

x + \frac{1}{x} = 10

and

x \neq 0

, then

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

= ___.

Q. If

x + x^{- 1} = 10, (x \neq 0)

then evaluate :

x^{2} + x^{- 2}

Q. If

{cot}^{- 1} (\frac{1 - x^{2}}{2 x}) + {cos}^{- 1} (\frac{1 - x^{2}}{1 + x^{2}}) = \frac{2 π}{3}, x > 0

x \neq 1

then

x =

Join BYJU'S Learning Program

If x+1x=10 and x≠0, then x2+1x2 = ___.

The correct option is B 98Given that, x+1x=10⟹(x+1x)2=100 Using the identity, (a+b)2=a2+b2+2ab, we have (x+1x)2=x2+1x2+2(x)(1x) ⟹100=x2+1x2+2 ⟹x2+1x2=100−2 ∴x2+1x2=98

If $x + \frac{1}{x} = 10$ and $x \neq 0$ , then $x^{2} + \frac{1}{x^{2}}$ = ___.