Question 79

If a-$$\frac{1}{a-3}$$=5 then the value of $$(a-3)^{3}-\frac{1}{(a-3)^{3}}$$

Solution

Let a -3 = x

a = x + 3

Therefore

a - $$\ \frac{\ 1}{a - 3}$$ = 5

x + 3 - $$\ \frac{\ 1} {x}$$ = 5

x - $$\ \frac{\ 1}{x}$$ = 2

$$\left(x-\ \frac{\ 1}{x}\right)^3\ =\ 2^3$$

$$x^3-\ \frac{\ 1}{x^3}-3.x.\frac{\ 1}{x}\left(x-\frac{\ 1}{x}\right)\ =\ 8$$

$$x^3-\frac{\ 1}{x^3}-3\left(2\right)\ =\ 8$$

$$x^3-\frac{\ 1}{x^3}\ =\ 14$$

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