SOLUTION: If a+b+c=0 Then find (a²+b²+c²)/(b²-ac)

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Question 1210384: If a+b+c=0
Then find (a²+b²+c²)/(b²-ac)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

if a%2Bb%2Bc=0, then a%2Bb=-c
=>c=-%28a%2Bb%29

find

%28a%5E2%2Bb%5E2%2Bc%5E2%29%2F%28b%5E2-ac%29.......substitute c
=%28a%5E2%2Bb%5E2%2B%28-%28a%2Bb%29%29%5E2%29%2F%28b%5E2-a%28-%28a%2Bb%29%29%29
=%28a%5E2%2Bb%5E2%2Ba%5E2+%2B+2+a+b+%2B+b%5E2%29%2F%28b%5E2%2Ba%5E2+%2B+a+b%29
=%282+a%5E2+%2B+2+a+b+%2B+2+b%5E2%29%2F%28a%5E2+%2B+a+b%2Bb%5E2%29
=%282+%28a%5E2+%2B++a+b+%2B++b%5E2%29%29%2F%28a%5E2+%2B+a+b%2Bb%5E2%29
=%282+%28a%5E2+%2B++a+b+%2B++b%5E2%29%29%2F%28a%5E2+%2B+a+b%2Bb%5E2%29.......simplify
=%282cross%28%28a%5E2+%2B++a+b+%2B++b%5E2%29%29%29%2Fcross%28%28a%5E2+%2B+a+b%2Bb%5E2%29%29
=2