Question

The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).

Answer 1

Answer:

(22, 9)

Step-by-step explanation:

The positive difference of two integers is 13. The sum of the larger number and the square of the smaller is 103. Give your solution(s) as ordered pair (larger, smaller).    I'll call the two integers a and b.

a - b  =  13        a + b² = 103

  +b     +b

a   =  13 + b    plug this into the second equation

a + b² = 103

(13+b) + b²  = 103    subtract 103 from both sides to get one side equal to zero

-103              -103

b² + b - 90 = 0      what factors (two numbers multiply) to -90 that also add up

                             to 1? The only two that work are -9 and 10.  

(b-9)(b+10) = 0      so  b-9 = 0     or    b+10 = 0

                                     +9  +9    or       -10   -10

                                     b = 9      or    b = -10 but both numbers must be positive

b = 9  and a = 13 + b so   a = 13 + 9 = 22

(22, 9)