# Math Help - Algebra

1. ## Algebra

If:
X+1/X=4

then what is the value of

X^3+1/x^3

2. Hi

Im just going to do this the classic/stupid way.

Solve for x in x+1/x=4 and you get x=1/3, then substitude it into the other equation and bam you got the answer.

THere's probably a better, more efficient way though...

Derg

3. Hello, Rimas!

This problem has a spectacular solution . . .

If $x + \frac{1}{x} \,=\,4$

then what is the value of $x^3 + \frac{1}{x^3}$

Cube the equation: . $\left(x + \frac{1}{x}\right)^3\;=\;4^3$

We have: . $x^3 + 3x^2\!\cdot\!\frac{1}{x} + 3x\!\cdot\!\frac{1}{x^2} + \frac{1}{x^3} \:= \:64\quad\Rightarrow\quad x^3 + 3x + \frac{3}{x} + \frac{1}{x^3}\:=\:64$

Then: . $x^3 + 3\underbrace{\left(x + \frac{1}{x}\right)}_\downarrow + \frac{1}{x^3} \:=\:64$
. . . . . . . $x^2 + 3(4) + \frac{1}{x^3} \:=\:64$

. . . . . . . . . $x^3 + \frac{1}{x^3} \:=\:52$