If a-$$\frac{1}{a-3}$$=5 then the value of $$(a-3)^{3}-\frac{1}{(a-3)^{3}}$$
Let a -3 = xÂ
    a = x + 3
Therefore
a - $$\ \frac{\ 1}{a - 3}$$ = 5
x + 3 - $$\ \frac{\ 1} {x}$$ = 5
x -Â $$\ \frac{\ 1}{x}$$ = 2
$$\left(x-\ \frac{\ 1}{x}\right)^3\ =\ 2^3$$
$$x^3-\ \frac{\ 1}{x^3}-3.x.\frac{\ 1}{x}\left(x-\frac{\ 1}{x}\right)\ =\ 8$$
$$x^3-\frac{\ 1}{x^3}-3\left(2\right)\ =\ 8$$
$$x^3-\frac{\ 1}{x^3}\ =\ 14$$
     Â
Create a FREE account and get:
