Question

(iii) a + b + c if a2 + b 2 + c2= 50 and
ab + bc + ca = 47​

Answer 1

$\huge\tt\orange{Given}$

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

$ab + bc + ca = 47$

$\huge\tt\orange{To~find}$

$a + b + c = ?$

$\huge\tt\red{Answer}$

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

Take 2 common.

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

Put the values.

${(a + b + c)}^{2} = 50 + 2(47)$

${(a + b + c)}^{2} = 50 + 94$

${(a + b + c)}^{2} = 144$

Taking square root on both the sides.

$a + b + c = \sqrt{144}$

$a + b + c = \sqrt{12 \times 12}$

$a + b + c = 12$

${\sf{\red{Answer~is~12}}}$