A 2 + B 2 A^{2} + B^{2}

Algebra Level 1

If A 2 + B 2 = C 2 A^{2} +B^{2} = C^{2} , does this mean that A + B = C A+B=C must be true?

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A Former Brilliant Member by A Former Brilliant Member

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3 solutions

Suppose that a + b = c . a + b = c.

( a + b ) 2 = c 2 a 2 + 2 a b + b 2 = c 2 a 2 + b 2 = c 2 − 2 a b (a + b)^2 = c^2 \\ a^2 + 2ab + b^2 = c^2 \\ \boxed{a^2 + b^2 = c^2 - 2ab}

Hence, if a + b = c , a 2 + b 2 ≠ c 2 . a + b = c, a^2 + b^2 \neq c^2.

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Im Opaaj
Jan 1, 2018

In general this is false, however there does exist 1 trivial solution. The triple (0,0,0) since of course 0+0=0 and 0^2+0^2=0^2.

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true 0,0,0 makes it true but i think the problem means distinct numbers

Austin Li - 11 months, 2 weeks ago
Sowmya Surapaneni
Dec 26, 2017

Pythagorean Theorem says "a² + b² = c²" which means a + b ≠ c.

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