解绝对值方程组.拜托了,各位.因为不知道解题步骤,所以求详细点:)

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解绝对值方程组.拜托了,各位.因为不知道解题步骤,所以求详细点:)

解绝对值方程组.拜托了,各位.因为不知道解题步骤,所以求详细点:)
解绝对值方程组.拜托了,各位.


因为不知道解题步骤,所以求详细点:)

解绝对值方程组.拜托了,各位.因为不知道解题步骤,所以求详细点:)
|ab|/2 = 2
|a - b| = 3
|ab| = 4
|a - b| = 3
ab = ± 4
a - b = ± 3
需要按以下四种情况分别讨论:
一、
ab = 4
a - b = 3
b = a - 3
a(a - 3) = 4
a² - 3a - 4 = 0
a1 = 4,b1 = 1 ;
a2 = - 1,b2 = - 4 .
二、
ab = 4
a - b = - 3
b = a + 3
a(a + 3) = 4
a² + 3a - 4 = 0
(a + 4)(a - 1) = 0
a3 = - 4,b3 = - 1 ;
a4 = 1,b4 = 4 ;
三、
ab = - 4
a - b = 3
ab = - 4
b = a - 3
a(a-3) = - 4
a² - 3a + 4 = 0
a² - 3a + 9/4 + 7/4 = 0
(a - 3/2)² = - 7/4
无解.
四、
ab = - 4
a - b = - 3
ab = - 4
b = a + 3
a(a+3) = - 4
a² + 3a + 4 = 0
a² + 3a + 9/4 + 7/4 = 0
(a + 3/2)² = - 7/4
无解.
所以,本题的解为:
a1 = 4,b1 = 1 ;
a2 = - 1,b2 = - 4 ;
a3 = - 4,b3 = - 1 ;
a4 = 1,b4 = 4 .