Question : What is the possible value of (a + b + c) – 3, if a2 + b2 + c2 = 9 and ab + bc + ca = 8?
Option 1: 5
Option 2: 3
Option 3: 9
Option 4: 2
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Correct Answer: 2
Solution :
Given: $a^2 + b^2 + c^2 = 9$ and $ab + bc + ca = 8$
We know, $(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)$
⇒ $(a+b+c)^2=9+2\times 8$
⇒ $(a+b+c)^2=9+16$
⇒ $a+b+c=\sqrt{25}=5$
$\therefore$ $(a+b+c)-3 = 5-3 = 2$
Hence, the correct answer is 2.
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