Question

if x+1÷x=4, then find x^3+1÷x^3 and x^4+1÷x^4

Answer 1

WE KNOW THAT (A+B)³ = A³+B³+3AB(A+B)

==> X³+1/X³+3.X.1/X [X+1/X]

==> X³+1/X³+3[4]

==>  X³+1/X³+12

==> X³+1/X³= -12

Answer 2

Answer:

194

Step-by-step explanation:

Given that,

x + 1/x = 4........(Equation) 1

Now,

Now,Do Square of Equation 1,

=> ( x + 1/x )² = 4²

=> x² + 1/x² + 2 = 16

=> x² + 1/x² = 16 - 2

=> x² + 1/x² = 14.......(Equation) 2

Hence,

The equation 2 is x² + 1/x² = 14

So,

Similarly here,

Do square of Equation 2,

=> ( x² + 1/x² )² = 14²

=> x⁴ + 1/x⁴ + 2 = 196

=> x⁴ + 1/x⁴ = 196 - 2

=> 194 (Answer)