Question

if A2+B2+c2=50and ab+BC+ca=47 find a+b+c
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Answer 1

Answer:

i think it is 25.

Step-by-step explanation:

Answer 2

$\huge{\mathbb{\red{ANSWER:-}}}$

Given :-

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

$\sf{ab + bc + ca = 47}$

To Find Out :-

$\sf{(a + b + c) = ?}$

Using Identity :-

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

Solution :-

$\sf{Putting \: the \: value \: of \: (a^{2}+b^{2}+c^{2}) \: and \: (ab+bc+ca)}$

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

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

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

$\sf{(a + b + c) =\sqrt{144}}$

$\sf{(a + b + c) = 12}$

Extra Identities :-

1)$\sf{(a+b+c)^{3} = a^{3} + b^{3} + c^{3} + 3a^{2}(b+c) + 3b^{2}(a+c) + 3c^{2}(a+b) + 6abc}$

2)$\sf{(a^{3} + b^{3} + c^{3} - 3abc) = (a + b + c)[a^{2} + b^{2} + c^{2} - (ab + bc + ca)]}$