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.

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) (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
=>
but since b+c=a
we get
from eq. 1 bc-a^2=-7
substituting this in above eq
we get
so Ans.
ans. a^2+b^2+c^2=14
RELATED QUESTIONS
If a+b+c = 8 and ab + bc + ac = 13 , find the value of (a^2) + (b^2) +... (answered by aliafzal14)

If a+b+c = 8 and ab + bc + ac = 13 , find the value of (a^2) + (b^2) +... (answered by aliafzal14)

Points A,B and C are collinear , where B falls between A &C. It is given that... (answered by ewatrrr)

Acute isosceles triangle ABC has vertices A(-2,-1), B(3,13), with point C on the line... (answered by greenestamps)

Complete the argument, giving a reason for each step. AB= BC Given AC= AB+BC... (answered by Edwin McCravy)

Find the value of x if A, B, and C are collinear points and B is between A and C.... (answered by jhunjiro)

is a =3, b=-2, and c=-5, evaluate the following expressions:... (answered by ikleyn)

If ac + bd = 19 and ad −bc = 94 , determine the value of (a^2 + b^2 )( c^2 + d^2... (answered by palanisamy)

In triangle ABC, AB + 2(BC) = BC + 2(AB) and AC + 2(AB) = AB + 2(AC). Classify triangle... (answered by richard1234)