Question

if a2+b2+c2 = 200 and ab+bc+ca = 28. find the value of a+b+c.

Answer 1

Here is your answer.

Answer 2

a + b + c = 16

Given: a^2 + b^2 + c^2 = 200 and ab + bc + ca = 28

To Find: The value of a + b + c

Solution: We know that,

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)$

We will put the values of a^2 + b^2 + c^2 and ab + bc + ca in the above equation:

Since, a^2 + b^2 + c^2 = 200, ab + bc + ca = 28

${(a + b + c)}^{2} = 200 + 2(28) \\ Opening the bracket of RHS:</p><p>{(a + b + c)}^{2} = 200 + 2 \times 28 \\ Using BODMAS rule, first we will perform multiplication:</p><p>{(a + b + c)}^{2} = 200 + 56 \\ </p><p>Now performing addition on RHS:</p><p>{(a + b + c)}^{2} = 256$

Now, to find the value of a + b + c, we have to find the square root of 256.

$a + b + c = \sqrt{256}$

The square root of 256 is 16.

Hence, a + b + c = 16

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