Question

$if \: a {}^{2} + b {}^{2} + c {}^{2} = 220 \: and \: ab + bc + ca = 4 \: then \: find \: the \: value \: of \: a + b + c$

Answer 1

We have,

=> a² + b² + c² = 220 ----- (1)

and, ab + bc + ca = 4 ----- (2)

Taking equation - (2)

=> ab + bc + ca = 4

Multiplying both sides by 2

=> 2(ab + bc + ca) = 8 ------ (3)

Now, adding equations (1) and (3), we get :-

=> a² + b² + c² + 2(ab + bc + ca) = 220 + 8

=> (a + b + c)² = 228

Taking square root on both sides :-

=> a + b + c = 2√57

Hope this helps.......