Evaluate x given the equation $x + \sqrt x = \sqrt 3$

Question

Given: $x + \sqrt x = \sqrt 3$
Evaluate: $x^3 - 1 / x^3$

@Peter Tamaroff . But even that will not ease the calculation right ? as we have only the form $ a^3 - b^3 $ — Harish Kayarohanam, Jul 30 '13 at 01:38
@HarishKayarohanam Yes it will, since $${x^3} + {x^{ - 3}} = {\left( {x + {x^{ - 1}}} \right)^3} - 3\left( {x + {x^{ - 1}}} \right)$$ — Pedro, Jul 30 '13 at 01:39
@Peter Tamaroff . But asked is $x^3 - x^{-3}$ right ? Am i missing something ? — Harish Kayarohanam, Jul 30 '13 at 01:45
@HarishKayarohanam Whoops! You can work out something similar, I got the signs wrong, sorry. — Pedro, Jul 30 '13 at 01:57
Sorry typo error, Peter is right, it should be $x + x^-1 = \sqrt {3}$ — user88226, Jul 31 '13 at 02:26

score 3 · Answer 1 · answered Jul 30 '13 at 01:27

3

HINT: we can solve $x+\sqrt{x}=\sqrt{3}$, using the quadratic formula. Just use $\sqrt{x}$ as the variable.

From there, it's just plugging in those values for $x$ into the second equation.

answered Jul 30 '13 at 01:27

Matt Groff

score 1 · Answer 2 · answered Jul 30 '13 at 01:32

1

Hint :

put $x=y^2$ and solve it by quadratic formula

answered Jul 30 '13 at 01:32

mnsh

2 Answers2