Question

If a^2 + b^2 + c^2 = 40 and ab + bc + ca = 30 then find the value of a + b + c

Answer 1

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Given: a²+ b²+ c²= 40, ab + bc + ac = 30

Find: a + b + c

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

(a + b + c)² = 40+ 2(ab+bc+ac) [Substituting the value and applying distributive property]

(a + b + c)² = 40+ 2(30) [Substituting the value]

(a + b + c)² = 40 +60

(a + b + c)² = 100

Applying the square root both sides

√((a + b + c)²) = √(100)

a + b + c = 10 :

Answer 2

Answer:

Given: a²+ b²+ c²= 40, ab + bc + ac = 30

Find: a + b + c

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

(a + b + c)² = 40+ 2(ab+bc+ac) [Substituting the value and applying distributive property]

(a + b + c)² = 40+ 2(30) [Substituting the value]

(a + b + c)² = 40 +60

(a + b + c)² = 100

Applying the square root both sides

√((a + b + c)²) = √(100)

a + b + c = 10 :