if x^2+1/x^2=7 find the value of x^3+1/x3 ...
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x^2 +1/x2 =7
add 2(x*1/x) both side,
x^2 + 1/x^2 +2 =7+2
(x+1/x)^2 = 9
x+1/x = root 9
x+1/x = 3
cube on both sides,
x^3+1/x^3 + 3(x*1/x)(x+1/x) = 3^3
x^3 +1/x^3 +3(3) = 27
x^3 +1/x^3 +9=27
x^3 +1/x^3 = 27-9
x^3 +1/x^3 = 18
i hope this will help
add 2(x*1/x) both side,
x^2 + 1/x^2 +2 =7+2
(x+1/x)^2 = 9
x+1/x = root 9
x+1/x = 3
cube on both sides,
x^3+1/x^3 + 3(x*1/x)(x+1/x) = 3^3
x^3 +1/x^3 +3(3) = 27
x^3 +1/x^3 +9=27
x^3 +1/x^3 = 27-9
x^3 +1/x^3 = 18
i hope this will help
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