Question

If a2 + b2 + c2 = 24 and ab + bc + ca = -4, then find
a+b+c​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

a + b + c = 4

Note:

• (a+b)² = a² + b² + 2ab

• (a-b)² = a² + b² - 2ab

• (a+b)(a-b) = a² - b²

• (a+b)³ = a³ + b³ + 3ab(a+b)

• (a-b)³ = a³ - b³ - 3ab(a-b)

• a³ + b³ = (a+b)(a² + b² - ab)

• a³ - b³ = (a+b)(a² + b² + ab)

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

Solution:

Given:

a² + b² + c² = 24

ab + bc + ca = - 4

To find:

a + b + c = ?

Now,

We know that ;

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

=> (a + b + c)² = 24 + 2×(- 4)

=> (a + b + c)² = 24 - 8

=> (a + b + c)² = 16

=> a + b + c = √16

=> a + b + c = 4

Hence,

The required value of (a + b + c) is 4 .