if x+1÷x=4, then find x^3+1÷x^3 and x^4+1÷x^4
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Answered by
3
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
Answered by
15
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)
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