2021AMC10数学竞赛选择题怎么准备 很重要的是学会一题多解

在AMC10的比赛中，有很多选择题，同学们课千万别小瞧这些选择题，因为他们就是你拿奖的关键因素，那么面对如此多的选择题，同学们该则呢么准备呢？下面给大家以选择题为例，教大家如何运用多种思维来选择正确的答案。

题目

Solution 1

Note that we can add the two equations to yield the equation：x^2+y^2-4x-4y+8=x+y+8，Moving terms gives the equation：x^2+y^2=5（x+y）。

We can also subtract the two equations to yield the equation：x^2-y^2-4x+4y=y-x。Moving terms gives the equation：x^2-y^2=3x-3y。Because x不等于y,we can divide both sides of the equation by  to yield the equation：x+y=3，Substituting this into the equation for  that we derived earlier gives x^2+y^2=5（x+y）=5(3)=(B)15

Solution 2 (Algebraic)

Subtract 4 from the left hand side of both equations, and use difference of squares to yield the equations： x=y(y-4)and y=x(x-4)。It may save some time to find two solutions, (0,0) and(5,5)  at this point.However, x=y  in these solutions.Substitute y=x(x-4)  into x=y(y-4) .This gives the equation：

x=x(x-4)(x^2-4x-4)，

which can be simplified to x(x^3-8x^2+12x+15)=0，Knowing x=0  and  x=5 are solutions is now helpful, as you divide both sides by x(x-5).This can also be done using polynomial division to find x=5  as a factor.This givesx^2-3x-3=0

Because the two equations x= y(y-4) and y=x(x-4) are symmetric, the  and  values are the roots of the equation, which are  and .

Squaring these and adding them together gives

Solution 3

By graphing the two equations on a piece of graph paper, we can see that the point where they intersect that is not on the line y=x  is close to the point (4,-1) or (-1,4).(-1^2)+4^2=17 and the closest answer choice to 1  is (B)15.

以上就是解题的3种方法，同学们在面对选择题的答案要是举棋不定时，不妨运用多种途径来找解决办法，不仅能够训练自己的竞赛思维还能够助力自己题目的正确率。马上就面临竞赛开考了，想拿奖就赶紧来橡沐吧，橡沐的竞赛复习班有着诸多一定能够给你最专业的帮助。

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