Question

find the value of ab + bc + ca if , a + b + c = 15 and a² + b² + c² = 77​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given :-}}}$

• a + b + c = 15

• a² + b² + c² = 77

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Value of ab + bc + ca = ?

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

$\underline{\:\textsf{As we know that :}}$

• ( a+b+c)² = a² + b² + c² + 2(ab+bc+ca)

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Then,

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

$\sf → (15)^2=77+2(ab+bc+ca)$

$\sf → 225=77+2(ab+bc+ca)$

$\sf → 225-77=2(ab+bc+ca)$

$\sf → 148=2(ab+bc+ca)$

$\sf → ab+bc+ca=74$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\underline{\textsf{ value of ab + bc + ca is \textbf{74}}}.$

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Answer 2

Answer:

$we \: \: have \: \: to \: \: use \: \: this \: \: identity \\ ( a + b + c {)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2ab +2 bc +2 ca \\ ({15})^{2} = 77 + 2(ab + bc + ca) \\ 225 = 77 + 2(ab + bc + ca) \\ 225 - 77 = 2(ab + bc + ca ) \\ 148/2 = ab + bc + ca \\ ab + bc + ca = 74 \\ answer \:$

I hope it will help you