Question : If (a + b + c) = 7 and ab + bc + ca = 12, find the value of a2 + b2 + c2.
Option 1: 29
Option 2: 31
Option 3: 27
Option 4: 25
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Correct Answer: 25
Solution : Given: ab + bc + ca = 12 (a + b + c) = 7 Squaring both sides, we get, ⇒ (a + b + c) 2 = 7 2 = 49 ⇒ a 2 + b 2 + c 2 + 2(ab + bc + ca) = 49 ⇒ a 2 + b 2 + c 2 = 49 – 2(ab + bc + ca) ⇒ a 2 + b 2 + c 2 = 49 – (2 × 12) = 49 – 24 = 25 Hence, the correct answer is 25.
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