Math, asked by kusumhns, 9 months ago

215 If a+b+c=6 and ab+bc+ca = 11, find a'^2+b^2+c^2

Answers

Answered by Anonymous
3

Answer :D

Given: a + b + c = 6, ab + bc + ca = 11

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

6² = a² + b² + c² + 2(11)

36 = a² + b² + c² + 22

a² + b² + c² = 14

Answered by prince5132
0

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GIVEN,

 =  > a + b  + c = 6 \\  =  > ab +  \: bc  + \: ca = 11

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TO FIND,

 =  > a ^{2}  + b ^{2}  + c ^{2}

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IDENTITY USED,

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

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SOLUTION,

 =  > a ^{2}  + b ^{2}  + c ^{2}  + 2ab + 2bc + 2ca = (a + b + c)  ^{2}  \\  \\ =  >  a ^{2}  + b ^{2}  + c ^{2}  + 2(ab + bc + ca) = (6) ^{2}  \\  \\  =  > a ^{2}  + b  ^{2}  + c ^{2}  + 2 \times 11 = 36 \\  \\  =  > a  ^{2}  + b ^{2}  + c ^{2}  + 22 = 36 \\  \\  =  > a ^{2}  + b ^{2}  + c ^{2}  = 36 - 22 \\  \\  =  > a ^{2}  + b ^{2}  + c ^{2}  = 14

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