A 2 + B 2 + C 2-ab-bc-ca = 0 is known, and a = b = C is proved

A 2 + B 2 + C 2-ab-bc-ca = 0 is known, and a = b = C is proved

It is proved that: ∵ A2 + B2 + c2-ab-ac-bc = 0 ∵ 2A2 + 2B2 + 2c2-2ab-2ac-2bc = 0 (a-b) 2 + (B-C) 2 + (A-C) 2 = 0 ∵ A-B = 0, B-C = 0, a-c = 0, ∵ a = B, B = C, C = a, ∵ a = b = C

Observe the following formula:
3²-1²=4×2
5²-3²=4×3
7²-5²=4×4
……
Then the 100th equation is____________ ;
The nth equation is____________ .

201²-199²=4×101
（2n+1）²-(2n-1）²=4（n+1）
The beauty of Mathematics

Math problems for grade seven (chapter on square difference formula)
2 * (3 + 1) (the square of 3) (the fourth power of 3 + 1). (2n power of 3 + 1)
2 * (3 + 1) (square of 3 + 1) (fourth power of 3 + 1)...... (2n power of 3 + 1)

2 * (3 + 1) (the square of 3 + 1) (the fourth power of 3 + 1). (2n power of 3 + 1)
=(3-1) (3 + 1) (the square of 3 + 1) (the fourth power of 3 + 1). (2n power of 3 + 1)
=(3's Square-1) (3's square + 1) (3's fourth power + 1). (3's 2n power + 1)
=(the fourth power of 3-1) (the fourth power of 3 + 1). (the 2nth power of 3 + 1)
=(2n power of 3-1) (2n power of 3 + 1)
=4N power of 3-1