$x \geq 0$ and $y$ are real numbers for which $y^2 \geq x(x + 1)$. Prove that: $(y - 1)^2 \geq x(x-1)$.
Problem
Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
Tags: inequalities, algebra
Source: IX International Festival of Young Mathematicians Sozopol, Theme for 10-12 grade
Tags: inequalities, algebra
$x \geq 0$ and $y$ are real numbers for which $y^2 \geq x(x + 1)$. Prove that: $(y - 1)^2 \geq x(x-1)$.