A math problem in junior high school (algebra) Let a, B, C satisfy a ^ 2 + B ^ 2 + C ^ 2 = 1, and prove that one of | A-B |, | B-C |, | C-A | must not exceed √ 2 / 2 (2 / 2 of the root sign)

A math problem in junior high school (algebra) Let a, B, C satisfy a ^ 2 + B ^ 2 + C ^ 2 = 1, and prove that one of | A-B |, | B-C |, | C-A | must not exceed √ 2 / 2 (2 / 2 of the root sign)

To prove the contrary, suppose that the sum of squares of | A-B |, | B-C |, | C-A | is greater than two-thirds of the root sign two, then we can get the contradiction