Question

if x2 +1/x2 =51 then find the value of x3-1/x3

Answer 1

x3-1/x3= (x-1/x) + 3 (x-1/x)
hope this helps!!!!!

Answer 2

Answer:

$\text{The value of }x^3-\frac{1}{x^3}\text{ is }\pm364$

Step-by-step explanation:

$\text{Given the value of }x^2+\frac{1}{x^2}=51\text{ we have to find the value of }x^3-\frac{1}{x^3}$

As by the identity

$(x-\frac{1}{x})^2=x^2-2x(\frac{1}{x})+\frac{1}{x^2}$

$(x-\frac{1}{x})^2=x^2+\frac{1}{x^2}-2$

$(x-\frac{1}{x})^2=51-2=49$

$(x-\frac{1}{x})=\sqrt{49}=\pm7$

Now by identity

$x^3-y^3=(x-y)^3+3xy(x-y)$

$x^3\(\frac{1}{x^3})=(x-\frac{1}{x})^3+3x(\frac{1}{x})(x-\frac{1}{x})$

$x^3-\frac{1}{x^3}=(x-\frac{1}{x})^3+3(x-\frac{1}{x})$

when x=7

$x^3-\frac{1}{x^3}=7^3+3(7)=343+21=364$

when x=-7

$x^3-\frac{1}{x^3}=(-7)^3+3(-7)=-343-21=-364$

$\text{hence, the value of }x^3-\frac{1}{x^3}\text{ is }\pm364$