If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2.

If a + b + c = 12 and ab + bc + ca = 22, find a² + b² + c².

Answer :

We know that

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

We can write it as

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

Substituting the values

a² + b² + c² = 12² – 2 (22)

By further calculation

a² + b² + c² = 144 – 44 = 100

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