Question : What is the value of a2 + b2 + c2, if a + b + c = 9 and ab + bc + ca = 23 ?
Option 1: 22
Option 2: 32
Option 3: 49
Option 4: 35
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Correct Answer: 35
Solution : Given: a + b + c = 9 and ab + bc + ca = 23 Squaring on both sides, ⇒ (a + b + c) 2 = 9 2 ⇒ a 2 + b 2 + c 2 + 2(ab + bc + ca) = 81 ⇒ a 2 + b 2 + c 2 = 81 – (2 × 23) = 81 – 46 = 35 Hence, the correct answer is 35.
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