Question

if a² + 2b = 7, b² + 4c = -7 and c² + 6a = -14, find a² + b² + c².

Answer 1

a^2+2b=7,b^2+4c=-7,c^2+6a=-14
addding all the three equations;we get
a^2+b^2+c^2+6a+4b+2c=7-7-14
a^2+b^2+c^2+6a+4b+2c=-14
a^2+b^2+c^2+6a+4b+2c+14=0
we can write this as;
a^2+6a+9+b^2+2b+1+c^2+4c+4=0
(a+3)^2+(b+1)^2+(c+2)^2=0
Hence; 
a+3=0,a=-3
b+1=0,b=-1
c+2=0,c=-2
therefore,a^2+b^2+c^2=(-3)^2+(-1)^2+(-2)^2
                                      =9+1+4
                                      =14....
a^2+b^2+c^2=14

Answer 2

Hii

Here is your answer -

we have to find the value of a² + b² + c²

Solution :

a² + 2b = 7

a² = 7 - 2b ....(1)

b² + 4c = -7

b² = -7 - 4c ....(2)

c² + 6a = -14

c² = -14 - 6a ....(3)

Substituting value of a² ,b² and c² in a² + b² + c²

a² + b² + c² = 7 - 2b - 7 - 4c - 14 - 6a

a² + b² + c² = - 6a - 2b - 4c - 14

a² + b² + c² = - 2(3a + b + 2c + 7)

value of a² + b² + c² is -2(3a + b + 2c + 7)

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