Question

if a^2+b^2+c^2=32 and ac+bc+ca =16 .find the value of a+b+c​

Answer 1

Correct Question :

If a² + b² + c² = 32 and ab + bc + ca = 16. Find the value of a + b + c.

Answer:

8

Step-by-step explanation:

Given :

• a² + b² + c² = 32

• ab + ab + ca = 16

We know that

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

Taking 2 common in RHS

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

Substituting the given values

⇒ ( a + b + c )² = 32 + 2( 16 )

⇒ ( a + b + c )² = 32 + 32

⇒ ( a + b + c )² = 64

Taking square root on both sides

⇒ a + b + c = √64 = 8

Therefore the value of a + b + c is 8.