Competition problem — Algebra — Maths Olympiad Prep

Library / /131 of 520

Algebra Difficulty 4.9 AIME Find the answer

2. The equation
$3 x^{3}+2 \sqrt{2} x^{2}-(17-9 \sqrt{2}) x-(6-5 \sqrt{2})=0$

has solutions
$x_{1}=$
$\qquad$
$, x_{2}=$
$\qquad$
$, x_{3}=$
$\qquad$ .

Your answer

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

Answer: $\frac{\sqrt{2}}{3}, \sqrt{2}-1,1-2 \sqrt{2}$ .

Want a route through all this instead of an archive? The track puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.