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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


Team Careers360 20th Jan, 2024
Answer (1)
Team Careers360 23rd Jan, 2024

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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