Question

If a^2+b^2+c^2=200 and ab+bc+ca=28 then find the value of a+b+c.​

Answer 1

$\huge\sf{solution:}$

Here, we use a suitable identity,

★ $\boxed{\sf{(a + b + c) ^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 ab+ 2bc + 2ca}}$

put the value of a + b + c = 200 and

ab + bc + ac = 28

$\implies$ $(a + b + c) ^{2} = 200 + 2 \times 28$

$\implies$ $(a + b + c) ^{2} = 200 + 56$

$\implies$ $(a + b + c) ^{2} = 256$

$\implies$ $(a + b + c) = \sqrt{256}$

$\implies$ $a + b + c = 16$

The required answer is 16.