Question

If a+b+c=9 and ab+bc+ca=23 then find a^2+b^2+c^2​

Answer 1

Answer:

ANSWER

Formula,

(a+b+c)

2

=a

2

+b

2

+c

2

+2ab+2bc+2ca

=a

2

+b

2

+c

2

+2(ab+bc+ca)

Given,

⇒9

2

=a

2

+b

2

+c

2

+2(23)

⇒81−46=a

2

+b

2

+c

2

∴a

2

+b

2

+c

2

=35

Answer 2

Answer:

${(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} \\ + 2ab + 2bc + 2ac \\ {9}^{2} = {a}^{2} + {b}^{2 } + {c}^{2} \\ + 2(ab + bc + ac)$

81 = a^2 + b^2 + c^2 +2(23)

81 = a^2 + b^2 + c^2 + 46

a^2 + b^2 + c^2 = 81 - 46 = 35