Question

If a square+b square+c square=16 and ab+bc+ca=10,find the value of a+b+c

Answer 1

Answer:

a square + b square + c square = 16

ab + bc + ca = 10

(a+b+c) Whole square = a square + b square + c square + 2(ab+bc+ca)

Replacing values

(a + b +c) whole square = 16 + 2*10

(a + b + c) Whole square = 16 +20

(a + b + c) whole square = 36

a + b + c = 6

Answer 2

Given,

a^2 + b^2 +c^2 = 16

and ab + bc + ca = 10

we have,

(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)

=> (a+b+c)^2 = 16 + (2 × 10)

=> (a+b+c)^2 = 16 + 20

=> (a+b+c) = √36

=> (a+b+c) = ±6 .

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