Is the absolute value of a greater than B a necessary and sufficient condition that the square of a is greater than the square of B? When a is - 5, B is 4 or - 4, is it not a sufficient and unnecessary condition?

Is the absolute value of a greater than B a necessary and sufficient condition that the square of a is greater than the square of B? When a is - 5, B is 4 or - 4, is it not a sufficient and unnecessary condition?

A ＞ B | is not a necessary and sufficient condition of a & # 178; > b & # 178
It can be seen from the question:
(1) When a ＞| B |,
∵ a ＞ |b| 》 0 ,=〉 a²> |b|² ≧ 0；
And ∵ B | - 178; = B | - 178;;
That is, a ＞ B | is a sufficient condition for a ＆ 178; > b ＆ 178;)
(2) When a & # 178; > b & # 178
∵ a² > b²≧ 0；
∴ |a|² > | b|²≧ 0；
=〉|a| ＞ |b| ≧ 0
=A ＞ B ≥ 0 (a ＞ B |)
Or a ＜ B ＜ 0 (can't get a ＞ B |)
(i.e. a & ﹥ 178; > b & ﹥ 178; is not a necessary condition for a ﹥ B ﹤)
To sum up, a ＞ B | is a sufficient and unnecessary condition for a ﹥ 178; > b ﹥ 178
The above is the analytical process of the problem, for mathematical problems, thinking must be rigorous, thinking must be clear, we not only need to know what the answer is, but also know why. Although I haven't studied mathematics for three years, I think the mathematical thinking I have practiced at the beginning is still very useful. Study hard, I wish you an ideal university_ ∩*)′

On the inequality x ^ 2 = 4 of X

Square of shift term x-m-4