Book Online Demo

Check Your IQ

Try Test

Courses

If $x − 1 x = 4,$ then the value of $x 4 + 1 x 4$ =[[1]].

see full answer

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

An Intiative by Sri Chaitanya

(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

x − 1 x = 4,

then the value of

x 4 + 1 x 4

= 322.
Here, we are given the value of an algebraic expression as follows,

x − 1 x = 4

.
Now, it can be observed that the expression

x 4 + 1 x 4

, has both terms raised to their fourth power.
So, to find its value, we will have to square the equation

x − 1 x = 4

, twice and then solve to get the required value. So, we have,

x − 1 x 2 = (4) 2 x − 1 x 2 = 16

Now, we know the following identity,

(a − b) 2 = a 2 + b 2 − 2 a b

(x) 2 + 1 x 2 − 2 × x × 1 x = 16 x 2 + 1 x 2 − 2 = 16

x 2 + 1 x 2 = 18

Now, squaring both sides of the above equation, we get

x 2 + 1 x 2 2 = (18) 2 x 2 + 1 x 2 2 = 324

Again, expanding using the identity

(a + b) 2 = a 2 + b 2 + 2 a b

, we get

x 2 2 + 1 x 2 2 + 2 × (x 2) × 1 x 2 = 324 x 4 + 1 x 4 + 2 = 324

x 4 + 1 x 4 + 2 − 2 = 324 − 2 x 4 + 1 x 4 = 322

Hence, the value of

x 4 + 1 x 4

is 322.

Watch 3-min video & get full concept clarity