Question

.If a+b+c=8 and ab+bc+ca=19, find a2 + b2 + c2.

Answer 1

answer of the Question is 48 when we multiple 8 by 6

Answer 2

$\mathfrak{\large{\underline{\underline{Given:-}}}}$

a + b + c = 8

ab + bc + ca = 19

$\mathfrak{\large{\underline{\underline{To find:-}}}}$

${a}^{2} + {b}^{2} + {c}^{2}$

$\mathfrak{\large{\underline{\underline{Solution:-}}}}$

The given question is solved by an identity :-

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

Now put the given value,

$\implies$ ${8}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(19)$

$\implies$ $64 - 38 = {a}^{2} + {b}^{2} + {c}^{2}$

$\implies$ ${a}^{2} + {b}^{2} + {c}^{2} = 26$