When a number is added to its multiple of 5 and its square, the sum of these three numbers is 91. Find the number.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 7.
Let the number be a.
According to the question;
a + 5a + a2 = 91
6a + a2 = 91
a2 + 6a - 91 = 0
⇒ a2 + 13a - 7a - 91 = 0
⇒ a(a + 13) - 7(a + 13) = 0
⇒ (a + 13)(a - 7) = 0
⇒ a = -13, 7
Out of the options, 7 is present. So, the number is 7.