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

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by zetteolalia

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by zetteolalia

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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.*

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.

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

130² = 16900

131 * 132 = 131²+131 = 17161+131 = 17292

Method 2: Quadratic Formula

1) 5700; x²-x-5700=0

x =

Therefore the two pages are 75 and 76.

x =

Therefore the two pages are 181 and 182.