Question

if x+1/x=4 then how to x4+1/x4=198​

Answer 1

x+1/x=4
Squaring Both side
(x+1/x)²=4²

As we know (a+b)²=a²+b²+2ab

Now Using this identity
➡️(x+1/x)²=16
➡️x²+1/x²+2×x×1/x=16
➡️x²+1/x²+2=16
➡️x²+1/x²=16-2
➡️x²+1/x²=14

And (a-b)²=a²+b²-2ab
Using this identity

Now ,squaring Both side

(x²-1/x²)²=14²
➡️x⁴+1/x⁴-2×x²+1/x²=196
➡️x⁴+1/x⁴=196+2
x⁴+1/x⁴=198

Answer 2

x+1/x= 4

x+1 = 4x

1=4x-x = 3x

so X = 1/3

(1/3)4 +1 /(1/3)4 = l.h.s.

= (4/3) +1 / (4/3)

=[(4+3)/3]/(4/3)

=[(7/3)/(4/3)]

= 7/4