Question

if a^2+b^2+c^2=250, andab+bc+ca=3 find a+b+c​

Answer 1

Answer:

16

Step-by-step explanation:

$a^{2}+b^{2}+c^{2}$ = 250

ab+bc+ca = 3

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

$(a+b+c)^{2}$ = 250+2(3)

                 = 250+6

    (a+b+c) = 256

                 = $\sqrt{256}$

                 = 16

Answer 2

Given,

$\bf \: {a}^{2} + {b}^{2} + {c}^{2} = 250 \\\bf ab + bc + ac = 3$

$\frak{To \: find : \purple{a + b + c =?} }$

$\bf \huge Solution \: \: : : : :$

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

$\tt \leadsto \: \: \tiny{a + b + c = \green{\sqrt{ {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) }} }$

$\frak{ \implies \sqrt{250 + 2(3)} } \\ \frak{ \implies \sqrt{250 + 6} } \\ \frak{ \implies \sqrt{256} = \red{16}}$

Therefore,

$\sf{Value \: \: of \: \: (a + b + c) \: \: is \: \: \red{16}.}$

$<marquee> MARK BRAINLIEST$