If x − 2/x = 3, then (x)^3 − 8/(x)^3 is equal to 1. 27 2. 36 3. 45 4. 54

We know that, (a - b) 3 = a 3 -3ab(a - b) - b 3 ⇒ a 3 - b 3 = (a - b) 3 + 3ab(a - b) Substituting values we get, Hence, Option 3 is the correct option.

Mathematics

If $x - \dfrac{2}{x} = 3, \text{ then } x^3 - \dfrac{8}{x^3}$ is equal to
27
36
45
54

Expansions

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Answer

We know that,

(a - b)³ = a³ -3ab(a - b) - b³

⇒ a³ - b³ = (a - b)³ + 3ab(a - b)

$\therefore x^3 - \dfrac{8}{x^3} = \Big(x - \dfrac{2}{x}\Big)^3 + 6\Big(x - \dfrac{2}{x}\Big)$

Substituting values we get,

$x^3 - \dfrac{8}{x^3} = 3^3 + 6 \times 3 \\[1em] = 27 + 18 \\[1em] = 45.$

Hence, Option 3 is the correct option.

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If $x - \dfrac{2}{x} = 3, \text{ then } x^3 - \dfrac{8}{x^3}$ is equal to
27
36
45
54

If $\dfrac{x}{y} + \dfrac{y}{x}$ = -1 (x, y ≠ 0) then the value of x³ - y³ is
1
-1
0
$\dfrac{1}{2}$

If a + b + c = 0, then the value of a³ + b³ + c³ is
0
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2abc
3abc