if x^4+1/x^4=47, find the value of x^3+1/x^3.
Answer (1)
29th Dec, 2020
Hello there,
Given that x^4 + 1/x^4 = 47, Now we have to find the value of x^3 + 1/x3.
So, we add and subtract 2 in the given equation
x^4 + 1/x4 +2 - 2 = 47, Now it can be written as
(x2)^2 + 1/(x2)^2 + 2. x^2.1/x^2 - 2 = 47
now, (x^2 + 1/x^2)^2 = 49
means, x^2 + 1/x^2 = 7, similarly adding and subtracting 2 we get that,
x + 1/x = 3,
And now the value of x^3 + 1/x3 is given as :
x^3 + 1/x^3 = (x+1/x)^3 - 3.x.1/x. ( x+1/x)
= 18
Hope it helps.
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