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Composite Function

If x = 3 + ...

Question

If $x = 3 + 3^{\frac{1}{3}} + 3^{\frac{2}{3}}$ , then find the value of $x^{3} - 9 x^{2} + 18 x$ .

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Solution

$⟶ x = 3 + 3^{1 / 3} + 3^{2 / 3}$
$(x - 3) = 3^{1 / 3} + 3^{2 / 3}$
$C_{0}$ be on both sides
$x^{3} - 27 - 3 (x) (3) (x - 3)$
$= 3 + 9 + 3 (3)^{1 / 3} (3)^{2 / 3} (x - 3)$
$x^{3} - 27 - 9 x + 27 x$
$= 12 + (3) (3) (x - 3)$
$x^{3} - 27 - 9 x + 27 x = 12 + 9 x - 27$
$x^{3} - 9 x + 18 x = 12$

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Similar questions

x = 3 + 3^{1 / 3} + 3^{2 / 3}

x^{3} - 9 x^{2} + 18 x =

x = 3 + 3^{\frac{1}{2}} + 3^{\frac{2}{3}}

x^{3} - 9 x^{2} + 18 x - 12

\frac{x^{2} + 1}{x} = 3 \frac{1}{3}

x > 1

, find the value of

x^{3} - \frac{1}{x^{3}}

.

Find the value of b, if (x - 3) is a factor of $x^{3} - 9 x^{2}$ - bx + 81 = 0

\frac{x^{2} + 1}{x} = 3 \frac{1}{3}

and x > 1 , then find

x^{3} - \frac{1}{x^{3}}

.

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