如果 x 是实数且 |x 2 – 2x + 3| = 11，那么可能的值是 |- x 3 + x 2 – x|包括
(一) 2、4
(二) 2, 14
(三) 4, 52
(四) 14, 52答案： (D)
解释：
Here we use the modulus property, which says:
|x| = x when x >= 0
|x| = -x when x < 0
i.e. range of a modulus function is always positive.
Now, given that |x^2 – 2x + 3| = 11, we can say that
x^2 – 2x + 3 = +11 ----------------(1)
and
x2 – 2x + 3 = -11------------------(2)
Solving 1st equation, we get real roots as 4 and -2.
Solving 2nd eq, we get imaginary roots, hence we ignore them.
Now, for eq |- x^3 + x^2 – x|, we put 4 and -2 in place of x.
putting x = 4, we get |-4^3 + 4^2-4| = |-64+16-4| = 52
putting x = -2 we get |-(-2)^3 + (-2)^2 - (-2)| = 14
so |- x^3 + x^2 – x| has possible values as 52 and 14 这个问题的测验