what are all the factor pairs that have products between 20 and 90 and have a difference of 1?

Question

Please help

Answer 1

Two consecutive factors can be represented by x and x+1, so we can write 20<=x(x+1)<=90. We can write two quadratic equations: x(x+1)-20>=0 and x(x+1)-90<=0. That is, x^2+x-20>=0 and x^2+x-90<=0, which become:

(x-4)(x+5)>=0 and (x-9)(x+10)<=0, so 4<=x<=9

So the pairs are 4,5; 5,6; 6,7; 7,8; 8,9; 9,10.

Answer 2

5x4=20      5-4=1

6x5=30      6-5=1

7x6=42       7-6=1

8x7=56       8-7=1

9x8=72        9-8=1

10x9=90       10-9=1