Question

If a + b + c = 12, ab + bc + ca = 44, then the value of a2 + b2 + c2 i

Answer 1

GIVEN :

a+b+c=12

ab+bc+ca=22

a^2+b^2+c^2=?

We know that

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ba)

(12)^2=a^2+b^2+c^2+2(22)

144=a^2+b^2+c^2+44

144-44=a^2+b^2+c^2

100=a^2+b^2+c^2

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Answer 2

Answer:

56

Step-by-step explanation:

$a + b + c = 12 \\ ab + bc + ca = 44 \\ {a}^{2} + {b}^{2} + {c}^{2} =? \\ since, \\ {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ = > {(12)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2 \times 44 \\ = > 144 = {a}^{2} + {b}^{2} + {c}^{2} + 88 \\ = > 144 - 88 = {a}^{2} + {b}^{2} + {c}^{2} \\ = > {a}^{2} + {b}^{2} + {c}^{2} = 56$