Question

if x= 3^1/3 + 3 ^-1/3 ,then 3x^3 -9x is

Answer 1

Answer: The answer is 10.

Step-by-step explanation: We are given that -

$x=3^{\frac{1}{3}}+3^{-\frac{1}{3}}.$

To find the value of  $3x^3-9x.$ For that, we need to evaluate the cube of both sides of the given equality, try to write the maximum expressions in terms of $x$ and then try to write the left hand side in the form $3x^3-9x.$.

We have

$x=3^{\frac{1}{3}}+3^{-\frac{1}{3}}\\\\\Rightarrow x^3 = (3^{\frac{1}{3}}+3^{-\frac{1}{3}})^{3} \\\\\Rightarrow x^3 = 3+3^{-1}+3\times 3^{\frac{1}{3}}+3\times 3^{-\frac{1}{3}}\\\\\Rightarrow x^3 = 3+\dfrac{1}{3}+3(3^{\frac{1}{3}}+3^{-\frac{1}{3}})\\\\\Rightarrow x^3  = 3+\dfrac{1}{3}+3x\\\\\Rightarrow 3x^3 = 9+1+9x\\\\\Rightarrow 3x^3-9x = 10.$

Thus, the answer is 10.

Answer 2

gekwpansyebwoansbdheiwpsndhe9wkwnwh