Question

if a+b+c = 8 and ab + bc + ca =16 then find a² + b²+ c² ​

Answer 1

Answer:-

Given:-

• (a + b + c) = 8
• ab + bc + ca = 16

To Find: Value of (a² + b² + c²)

We know,

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

Or,

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

[Taking 2 common in the RHS.]

Putting the values:-

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

→ (8)² = a² + b² + c² + 2(16)

→ a² + b² + c² = 64 - 32

→ a² + b² + c² = 32

∴ a² + b² + c² = 32.

Answer 2

Answer:

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca

(a+b+c)^2 = a^2 + b^2 + c^2 + 2 ( ab+bc+ca)

(8)^2 = a^2 + b^2 + c^2 + 2(16)

64 = a^2 + b^2 + c^2 + 32

64 - 32 = a^2 + b^2 + c^2

32 = a^2 + b^2 + c^2