One positive number is 4 larger than another number. The sum of their squares is 106. Find the numbers.
A) 1, 5
B) 8, 11
C) 5, 9
D) 6, 10

Question

Quizplus · Accepted Answer

Let x be the smaller number, then the larger number is x + 4. From the given information, we have the equation x^2 + (x+4)^2 = 106. Expanding and simplifying, we get 2x^2 + 8x - 90 = 0. Factoring out 2, we get x^2 + 4x - 45 = 0. The factors of -45 that differ by 4 are -5 and 9, so x = -9 or x = 5. Since we are looking for a positive number, we choose x = 5, which gives the larger number as x + 4 = 9. Therefore, the numbers are 5 and 9, which is choice C.

One Positive Number Is 4 Larger Than Another Number