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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