How many values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number? Please don't paste it from Baidu. Their method is either not good or they can't understand it. It's better to draw inferences from one instance. If it's especially good, add it to 50 points, Here's how to eat beef noodles First, let m ^ 4-m ^ 2 + 4 = k ^ 2 Then m ^ 4-m ^ 2 = k ^ 2-4, so (m ^ 2-m) (m ^ 2 + m) = (K-2) (K + 2) ① If m ^ 2 and m are not zero and are integers, then we can get m ^ 2-m = K-2 or m ^ 2 + M = K + 2 (this is actually (a + b) (a-b) = (c + D) (C-D), where ABCD is a positive integer. If you give a value, you will find that a = C and B = D at any time ② If m ^ 2 or M = 0, then K does not care about it, because in any case K will have a value that meets the conditions of the problem, so directly solving m ^ 2-m = 0 or m ^ 2 + M = 0, we can get m = 0 or plus or minus 1, because m is a natural number, so m = 0,1,2

How many values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number? Please don't paste it from Baidu. Their method is either not good or they can't understand it. It's better to draw inferences from one instance. If it's especially good, add it to 50 points, Here's how to eat beef noodles First, let m ^ 4-m ^ 2 + 4 = k ^ 2 Then m ^ 4-m ^ 2 = k ^ 2-4, so (m ^ 2-m) (m ^ 2 + m) = (K-2) (K + 2) ① If m ^ 2 and m are not zero and are integers, then we can get m ^ 2-m = K-2 or m ^ 2 + M = K + 2 (this is actually (a + b) (a-b) = (c + D) (C-D), where ABCD is a positive integer. If you give a value, you will find that a = C and B = D at any time ② If m ^ 2 or M = 0, then K does not care about it, because in any case K will have a value that meets the conditions of the problem, so directly solving m ^ 2-m = 0 or m ^ 2 + M = 0, we can get m = 0 or plus or minus 1, because m is a natural number, so m = 0,1,2

A: there are three values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number, that is, when m is equal to 0, 1 or 2, there are three values of natural number m that make m ^ 4-m ^ 2 + 4 a complete square number, that is, when m is equal to 0, 1 or 2, m ^ 4-m ^ 2 + 4 & nbsp; are 4, 4 and 16, which are respectively ± 2, ± 2, ± 4