The average of a positive number, its square and 3 is 5. Find the number.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 3
The average of three quantities is their sum divided by 3, so the number, its square and 3 must add up to \(3\times5=15\).
Assuming the number to be \(x\):
\(x+x^2+3=15\)
\(x^2+x-12=0\), that is, \((x+4)(x-3)=0\)
\(x=3\); the other root, \(-4\), is rejected because the number is positive
Shortcut:
Test the options in \(x+x^2+3=15\): for 3, \(3+9+3=15\)