Question

If
\[\huge x=\sqrt[3]{7+5\sqrt{2}}-\frac{ 1 }{ \huge \sqrt[3]{7+5\sqrt{2}} }\]

then find the value of
\[\huge x ^{3}+3x-14\]

Answer 1

@ganeshie8 @zepdrix

Answer 2

say \[\large x = t - \dfrac{1}{t}\]

\[\begin{align} \\ x^3 + 3x-14 &= \left(t-\dfrac{1}{t}\right)^3 - 3 \left(t-\dfrac{1}{t}\right)-14\\~\\&=t^3 - \dfrac{1}{t^3} -3(t - \dfrac{1}{t}) +3(t - \dfrac{1}{t})-14 \\~\\
&=t^3 - \dfrac{1}{t^3}-14 \end{align} \]

Answer 3

plugin \(t^3 = 7 +5\sqrt{2} \) above ^^

Answer 4

oh i got it

Answer 5

there os a simpler way

Answer 6

how?

Answer 7

nvm, it wont work >.<

Answer 8

what was the idea , it's ok

Answer 9

i think you should get 0 or 1 in the end as final answer

Answer 10

perfect :)

Answer 11

corrected typo

say \[\large x = t - \dfrac{1}{t}\]

\[\begin{align} \\ x^3 \color{red}{+} 3x-14 &= \left(t-\dfrac{1}{t}\right)^3 \color{red}{+} 3 \left(t-\dfrac{1}{t}\right)-14\\~\\&=t^3 - \dfrac{1}{t^3} -3(t - \dfrac{1}{t}) +3(t - \dfrac{1}{t})-14 \\~\\
&=t^3 - \dfrac{1}{t^3}-14 \end{align} \]

Answer 12

thanks