If $$x = 5 - \frac{1}{x} $$, then what is the value of $$x^{5} + \frac{1}{x^{5}}$$?
Given : $$x=5-\frac{1}{x}$$
=> $$x+\frac{1}{x}=5=k$$
Now, $$x^5+\frac{1}{x^5}=[(x^3+\frac{1}{x^3})\times(x^2+\frac{1}{x^2})]-(x+\frac{1}{x})$$
= $$[(x+\frac{1}{x})^3-3(x+\frac{1}{x})\times(x+\frac{1}{x})^2-2(x)(\frac{1}{x})]-(x+\frac{1}{x})$$
= $$[(k^3-3k)\times(k^2-2)]-(k)$$
= $$[(125-15)\times(25-2)]-(5)$$
= $$(110\times23)-5$$
= $$2530-5=2525$$
=> Ans - (C)
Create a FREE account and get:
