Question

the value of (a+b+c) when a*a+b*b+c*c=29 and ab+bc+ca=26​

Answer 1

$\bf \red { solution}$

Given (a + b + c) = 9 and (ab + bc + ca) = 26 (a + b + c)2 = 92

⇒ a2 + b2 + c2 + 2(ab + bc + ca) = 81

⇒ a2 + b2 + c2 + 2(26) = 81

⇒ a2 + b2 + c2 + 52 = 81

⇒ a2 + b2 + c2 = 81 − 52 = 29

Answer 2

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

$(a + b + c) {}^{2} = 29 + 2(26)$

$a + b + c = \sqrt{29 + 52}$

$a + b + c = \sqrt{81}$

$a + b + c = 9$