SOLUTION: If a^2 – bc = 7, b^2 + ac = 7, c^2 + ab = 7, then determine the value of a^2 + b^2 + c^2.

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Question 254828: If a^2 – bc = 7, b^2 + ac = 7, c^2 + ab = 7, then determine the value of a^2 + b^2 + c^2.
Answer by vksarvepalli(154) About Me  (Show Source):
You can put this solution on YOUR website!
a^2 – bc = 7-------- 1
b^2 + ac = 7-------- 2
c^2 + ab = 7-------- 3
equating 1 and 2
then 2 and 3
then 3 and 1
we get either a=b+c
or b=c=-a
but if b=c=-a the given equations will not satisfy
so a=b+c
now add the three equations 1,2 & 3
we get a%5E2%96bc%2Bc%5E2%2Bab%2Bb%5E2%2Bac=21
=> a%5E2%2Bb%5E2%2Bc%5E2=21%2Bbc-a%28b%2Bc%29
but since b+c=a
we get a%5E2%2Bb%5E2%2Bc%5E2=21%2Bbc-a%5E2
from eq. 1 bc-a^2=-7
substituting this in above eq
we get a%5E2%2Bb%5E2%2Bc%5E2=21-7
so a%5E2%2Bb%5E2%2Bc%5E2=14 Ans.
ans. a^2+b^2+c^2=14