Real Roots of the System

Algebra Level 2

Find the number of the real root pairs that satisfy the system below.

$\begin{cases} x = y^2 + y + 1 \\ 5y=2-x-x^2 \end{cases}$

Source: National Turkish Mathematics Olympiad -- Phase 1

4 3 1 2 None of the others

1 solution

A Former Brilliant Member
Oct 17, 2019

Substituting for $x$ in the second equation we get $y(y^3+2y^2+4y+8)=0$ . This yields two real values of $y$ , namely $y=0$ and $y=-2$ , corresponding to which the two real values of $x$ are $1$ and $3$ . Therefore there are $\boxed 2$ real pairs of solutions.

Real Roots of the System

1 solution

0 pending reports