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.
