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.
Related Questions
Question : What is the possible value of (a + b + c) – 3, if a2 + b2 + c2 = 9 and ab + bc + ca = 8?
Question : If $a+b+c$ = 6 and $ab+bc+ca$ = 11, then the value of $bc(b+c)+ca(c+a)+ab(a+b)+3abc$ is:
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