Book Online Demo

Check Your IQ

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

Q.

If it is given that ( $x + \frac{1}{x}$ ) =4 find the value of ( $x^{4} + \frac{1}{x^{4}}$ )

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

a

120

b

194

c

160

d

140

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

Concept- Calculating the total of both terms raised to the power of four is necessary. In order to do that, we must first square both sides of the equation and solve it in order to obtain the sum (

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

). Since the terms in (x+

\frac{1}{x}

) are reciprocal of one another, the ′2ab′ term in

{(a + b)}^{2}

will be canceled, leaving only ′2′. Finally, we must square both sides of the equation once more and solve in order to obtain the value of the required sum in a manner similar to that described above.
Given, (x+

\frac{1}{x}

) =4

{(x + \frac{1}{x})}^{2} = 4^{2}

x^{2} + \frac{1}{x^{2}} + 2 x \frac{1}{x} = 16

x^{2} + \frac{1}{x^{2}} = 16 - 2

x^{2} + \frac{1}{x^{2}} = 14_____(1)

Squaring equation 1

({x^{2} + \frac{1}{x^{2}})}^{2} = 14^{2}

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

=

14^{2}

{(x^{2})}^{2} + {(\frac{1}{x^{2}})}^{2} + 2 . x^{2} . \frac{1}{x^{2}} = 196

x^{4} + \frac{1}{x^{4}} + 2 = 196

x^{4} + \frac{1}{x^{4}} = 194

Hence, the correct answer is option 2) 194.

Watch 3-min video & get full concept clarity

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Get Expert Academic Guidance – Connect with a Counselor Today!

Related Blogs

Get ₹ 1 crore* worth scholarship for JEE / NEET / Foundation

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th

Not sure what to do in the future? Don’t worry! We have a FREE career guidance session just for you!