if x²+1/x²=98,find the value of x³+1/x³
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x^2 + 1/x^2 = 98
On adding 2 in both sides, we get
x^2 + 1/x^2 + 2 = 98 + 2
=> x^2 + 1/x^2 + 2 (x)(1/x) = 100
=> ( x + 1/x)^2 = 100
=> x + 1/x = 10 -------(1)
On curbing both sides, we get
x^3 + 1/x^3 + 3 (x) (1/x) (x +1/x) = 1000
=> x^3 + 1/x^3 + 3 (10) = 1000
=> x^3 + 1/x^3 + 30 = 1000
=> x^3 + 1/x^3 = 970
On adding 2 in both sides, we get
x^2 + 1/x^2 + 2 = 98 + 2
=> x^2 + 1/x^2 + 2 (x)(1/x) = 100
=> ( x + 1/x)^2 = 100
=> x + 1/x = 10 -------(1)
On curbing both sides, we get
x^3 + 1/x^3 + 3 (x) (1/x) (x +1/x) = 1000
=> x^3 + 1/x^3 + 3 (10) = 1000
=> x^3 + 1/x^3 + 30 = 1000
=> x^3 + 1/x^3 = 970
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