Question

Find the value of a^2+b^2+c^2 when a+b+c = 8 and ab+bc+ac = 25

Answer 1

Answer:

$(a + b + c) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2ab + 2bc \\ + 2ca \\ (8) {}^{2} = a {}^{2} + b {}^{2} + c {}^{2} + 2(ab + bc + ca) \\ 64 = a {}^{2} + b {}^{2} + c {}^{2} + 2(25) \\ a {}^{2} + b {}^{2} + c {}^{2} + 50 = 64 \\ a {}^{2} + b {}^{2} + c {}^{2} = 64 - 50 = 14$

Answer 2

(a + b+ c)² = a² + b² + c² + 2ab + 2bc +2ca

(8)²= a² + b² + c² + 2(ab+ bc + ca)

64=a² + b² + c² + 2(25)

64=a² + b² + c² + 50

64-50=a² + b² + c²

14=a²+b²+c²

a²+b²+c²=14

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