Question

If a² + b² + c² = 38 and ab + bc + ca = 31, find the value of a + b + c.

Answer 1

Answer:

Here is your answer! Hope it helps you!

Step-by-step explanation:

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

=38=a+b+c-2*31

38=a+b+c-62

-a+b+c=-62-38

-a+b+c=-24

a+b+c=24

Answer 2

Answer:

The value of a+b+c = 10

Step-by-step explanation:

Given,

a² + b² + c² = 38

ab + bc + ca = 31

To find,

The value of a+b+c

Recall the formula

(a+b+c)² = a² + b² + c² + 2ab+2bc+2ac

Solution:

We have the formula,

(a+b+c)² = a² + b² + c² + 2ab+2bc+2ac

(a+b+c)² = a² + b² + c² + 2(ab+bc+ac) ----------------(1)

Substituting the value of  a² + b² + c² = 38 , ab + bc + ca = 31 in equation(1)

(a+b+c)² = 38 + 2(31)

=38+62

= 100

a+b+c = √100 = 10

∴ The value of a+b+c = 10

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