Question

if a + b + C is equal to 14 and a square + b square + c square is equal to 74 find the value of a b + BC + CA​

Answer 1

Answer :-

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Given :-

a + b + c = 14

a² + b² + c² = 74

To find :- ab + bc + ca

Salutation :-

a² + b² + c² = 74

( a + b + c )² - ( 2ab + 2bc + 2ca ) = 74

( 14 )² - 2 ( ab + bc + ca ) = 74

196 - 2 ( ab + bc + ca ) = 74

- 2 ( ab + bc + ca ) = 74 - 196

- ( ab + bc + ca ) = - 122 / 2

( ab + bc + ca ) = 61

•°• Required answer is 61

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Thanks!

Answer 2

$\underline{\bf{Given}}$:-

a+b+c =14

a^2 +b^2 +c^2 =74

$\underline{\bf{To\:Find}}$:-

ab+bc+ca

$\underline{\bf{Answer}}$:-

61

$\underline{\bf{Solution}}$:-

We know the identity

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

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

So,

(14)^2 = 74 +2(ab+bc+ac)

196=74 +2(ab+bc+ac)

196-74=2(ab+bc+ac)

122=2(ab+bc+ac)

122/2 = ab+bc+ac

61 =ab+bc+ac