# To what pages must narding open his book so that the product of the book two facing pages is 5 700?17 292?

1
by zetteolalia

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

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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.