Question

f a+b+c=5 and ab+bc+ca then find the value of a^2+b^2+c^2

Answer 1

☆ Correct Question :-

$\\ \bf If \: \: a+b+c=5 \: \: and \: \: ab+bc +ca=10. \\ \bf \: Then, \: find \: the \: value \: \: of \: \: a^2+b^2+c^2.$

■ Solution :-

Given,

$\: \: \tt a + b + c = 5 \\ \tt ab + bc + ca = 10$

To find :-

$\tt {a}^{2} + {b}^{2} + {c}^{2} = \: ?$

NOW,

$= > \huge\bf a + b + c = 5 \\ = > \large \bf {(a + b + c)}^{2} = {(5)}^{2} \\ = > \tiny \bf {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 25 \\ = > \tiny \bf {a}^{2} + {b}^{2} + {c}^{2} + 2(10) = 25 \\ = > \tiny \bf {a}^{2} + {b}^{2} + {c}^{2} + 20 = 25 \\ = > \tiny \bf {a}^{2} + {b}^{2} + {c}^{2} = 25 - 20 \\ = > \red{ \bf {a}^{2} + {b}^{2} + {c}^{2} =5}$