1.

If a+b+c=7 and ab+bc+ca=22 find a^2+b^2+c^2

Answer»

Given:

  • a+b+c=7
  • ab+bc+ca=22

To find out:

Find a² + b² + c²

Formula USED:

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

Solution:

We know that,

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

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

⇒ ( 7 ) ² = a² + b² + c² + 2 × 22

⇒ 49 = a² + b² + c² + 44

⇒ a² + b² + c² = 49 - 44

⇒ a² + b² + c² = 5


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