AMC 8 2022 Problem 2

AMC8 2022 年第 2 题

表达式与运算★☆☆☆☆

Consider these two operations as shown below. What is the value of

(5 \, \blacklozenge \, 3) \, \bigstar \, 6

考虑下图所示的两种运算。那么

(5 \, \blacklozenge \, 3) \, \bigstar \, 6

的值是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

We can find a general solution to any

((a \, \blacklozenge \, b) \, \bigstar \, c)

((a \, \blacklozenge \, b) \, \bigstar \, c)

=((a^2-b^2) \, \bigstar \, c)

=(a^2-b^2-c)^2

=a^4+b^4-(a^2)(b^2)-2(a^2)(c)-(b^2)(a^2)+2(b^2)(c)+c^2

=5^4+3^4-(5^2)(3^2)-2(5^2)(6)-(3^2)(5^2)+2(3^2)(6)+6^2

=625+81-225-300-225+108+36 =100 "This is very time wasting" There are unnecessary equations ':( solution 2 guys To time wasting just go to solution 2

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