if x+1/x=4 find the value of
x^2+1/x^2
x^3+1/x^3
Answers
Answer:
x³ + 1/x² = 54
Step-by-step explanation:
Given, x + 1/x = 4.........(1) and x² + 1/x³ = 12..........(2)
On squaring both sides in eq. (1) Put x² = 14 - 1/x² in eq. (2)
(x + 1/x)² = 4² 14 - 1/x² + 1/x³ = 12.....(4)
x² + 1/x² = 16 - 2
x² = 14 - 1/x²
On cubing both sides in eq. (1)
(x + 1/x)³ = 4³
x³ + 1/x³ + 3x +3/x = 64
x³ + 1/x³ = 64 - 3(x + 1/x).......(3)
From eq. (1) and (3) Put 1/x³ = 52 - x³ in eq. (4)
x³ + 1/x³ = 64 - 3×4 14 - 1/x² + 52 - x³ = 12
x³ + 1/x³ = 52 x³ + 1/x² = 54
1/x³ = 52 - x³
Step-by-step explanation:
thats all plz do brainlest
