Question

If a, b and c are real numbers such that a2 + 2b = 7, b2 + 4c = -7 and c2 + 6a = -14, then find the value of
a2 + b2 + c2
(A) 14
(B) O
(C) 7
(D) cannot be determined​

Answer 1

• Step-by-step explanation:

To Find :

• 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)

$\large\dag \large { \red{\underline{\bf{Hence }}}}$

$\blue{\textbf{value of a² + b² + c² is -2(3a + b + 2c + 7) }}$

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Answer 2

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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