Question : If a + b + c = 10 and a2 + b2 + c2 = 48, then the value of ab + bc + ca is _______.
Option 1: 25
Option 2: 26
Option 3: 24
Option 4: 18
Correct Answer: 26
Solution :
Given: a + b + c = 10 and a
2
+ b
2
+ c
2
= 48
Using the formula: (a + b + c)
2
= a
2
+ b
2
+ c
2
+ 2ab + 2bc + 2ca
⇒ (10)
2
= 48 + 2(ab + bc + ca)
⇒ 100 – 48 = 2(ab + bc + ca)
$\therefore$ ab + bc + ca = $\frac{52}{2}$ = 26
Hence, the correct answer is 26.
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