Question

if a²+b²+c²=50 and ab+bc+ca=46, find a+b+c
​

Answer 1

Step-by-step explanation:

We know that

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

Given,

${a}^{2} + {b}^{2} + {c}^{2} = 50$

Also, ab+bc+ca=46

So,

${(a + b + c)}^{2} = 50 + 2(46) = 142$

So,

$a + b + c = \sqrt{142}$

Thank you

Answer 2

$\huge\red{\mathbb{ QUESTION}}$

★ ★ a²+b²+c²=50 and ab+bc+ca=46, find a+b+c

$\huge\pink{ \mathbb{SOLUTION} \implies: }$

$\huge \bf\ using \: formula \leadsto: \\ \\ \bf\ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ba)$

$\sf\ {a}^{2} + {b}^{2} + {c}^{2} =50 \: and \: ab+bc+ca=46 \\ \\ \bf\ \implies: {(a + b + c)}^{2} =50 + 2(46) \\ \\ \bf\ \implies: {(a + b + c)}^{2} = 50 + 92 \\ \\ \bf\ \implies:{(a + b + c)}^{2} = 142 \\ \\ \bf\ \implies: a + b + c = \sqrt{142} \\ \\ \bf\ \implies:a + b + c = 11 \sqrt{21}$