Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 4.7 AIME Find the answer

1. Given that $a$ , $b$ , $c$ are three consecutive odd numbers in increasing order. Then the value of $a^{2}-2 b^{2}+c^{2}$ is $\qquad$

Your answer

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

Solution

$-1.8$ .
Since $a=b-2, c=b+2$ , then,
$\begin{array}{l} a^{2}-2 b^{2}+c^{2} \\ =b^{2}-4 b+4-2 b^{2}+b^{2}+4 b+4=8 . \end{array}$

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