Find the value of a²+b²+c² when a+b+c=✓17 and ab+bc+ca=2
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Answer:
a² + b² + c² = 13
Step-by-step explanation:
We know that:
(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
⇒ (a + b + c)² = a² + b² + c² + 2( ab + bc + ca )
⇒ (√17)² = a² + b² + c² + 2( 2 )
⇒ 17 = a² + b² + c² + 4
⇒ a² + b² + c² = 17 - 4
∴ a² + b² + c² = 13
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