Answers

2015-06-11T13:33:54+08:00

This Is a Certified Answer

×
Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
I don't know if you are really Elementary so I will show you two ways.

Method 1: Guess and Check
Whenever we need to look for two consecutive numbers with a product of ___. We simply look for a perfect square nearest it. We just keep testing the nearest.

1) 5700. This is equal to 57 * 10² and the nearest perfect square to 57 is 7² or 49 so:
70² = 4900  We look for a number much closer to 5700
75² = 5625  This is close already so we test 75*76
75*76 = 75²+75 = 5625+75 = 5700   So the two pages are 75 and 76.

2) We do the same for 17292. We round this off to 17000=170*10², the nearest square to 170 is 13² or 169 so,
130² = 16900  This is close so we try the next square:
131² = 130²+(131-130)(131+130) = 16900+261 = 17161 
131 * 132 = 131²+131 = 17161+131 = 17292  So the two pages are 131 and 132.

Method 2: Quadratic Formula
This is actually more complicated, but if ever your teacher wants you to solve it systematically I will show you how. We let the bigger number be x. In the quadratic formula we do not consider the negative value.
x(x-1)=____ ; x²-x-____ = 0

1) 5700; x²-x-5700=0
x = 1 + √[(5700*4)+1] = 1 + √22801 = 1 + 151 = 76
                 2                       2                2
Therefore the two pages are 75 and 76.

2) 17292; x²-x-17292=0
x = 1 + √[(17292*4)+1] = 1 + √69169 = 1 + 263 = 182
                  2                        2                2
Therefore the two pages are 181 and 182.

0