比较下列各题中两式值的大小 .

题目

比较下列各题中两式值的大小 .
1.x(x-y)与y(x-y) (x不等于Y)
2.(3a+1)(a+1)与2(a+1)平方-3
3.(t+1)(t-5)=(t-2)平方.

答案

1.x(x-y) - y(x-y) = (x-y)(x-y) = (x-y)^2 > 0 (因x不等于y)
x(x-y) 〉 y(x-y)
2.(3a+1)(a+1) -[2(a+1)^2 -3]
= 3a^2 + 4a + 1 -(2a^2 + 4a +2 -3)
= a^2 + 2 > 0
(3a+1)(a+1) > 2(a+1)^2 -3
3.(t+1)(t-5) - (t-2)^2
= t^2 -4t -5 -(t^2 -4t +4)
= -9 < 0
(t+1)(t-5) < (t-2)^2