System of equations
Find the sum of the real roots
can you solve it in 60 seconds
The answer is -6.
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1 solution
Add all three equations to get: a 2 + 6 a + b 2 + 2 b + c 2 + 4 c = − 1 4
( a + 3 ) 2 + ( b + 1 ) 2 + ( c + 2 ) 2 = 0
And because all squares are non-negative, there is only one solution:
( a + 3 ) = 0 ; ( b + 1 ) = 0 ; ( c + 2 ) = 0
Or a = − 3 ; b = − 1 and c = − 2 as the only real solution.
a + b + c = − 6