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IF X∧2+1/X∧2=7 , FIND THE VALUE OF X∧3+1/X∧3PLS ANSWER ITS AN EMERGENCY THOSE WHO ARE ANSWER IS BEST I WILL MARK AS BRANLIEST

Answer»

Given Equation is x^2 + 1/x^2 = 7.


It can be written as:


= > x^2 + 1/x^2 + 2 = 9


It can be written as:


= > x^2 + 1/x^2 + 2 * x * 1/x = 9


It is in the form of a^2 + B^2 + 2ab = > (a + b)^2


= > (x + 1/x)^2 = 9


= > x + 1/x = 3.


On CUBING both SIDES, we get


= > (x + 1/x)^3 = (3)^3


We know that (a + b)^3 = a^3 + b^3 + 3ab(a + b).


= > x^3 + 1/x^3 + 3 * x * 1/x(x + 1/x) = 27


= > x^3 + 1/x^3 + 3(3) = 27


= > x^3 + 1/x^3 + 9 = 27


= > x^3 + 1/x^3 = 27 - 9


= > \boxed {x^{3} + \frac{1}{x^3} = 18}}



Hope this helps!


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