题目信息
What is the value of x ?
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B:Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C:BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D:EACH statement ALONE is sufficient.
E:Statements (1) and (2) TOGETHER are NOT sufficient.
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正确答案：
A:Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Algebra Simplifying algebraic expressions
If x4 + x2 + 1 =
, then 
is its own reciprocal. The only numbers that are their own reciprocals are −1 and 1. Since even powers of x are nonnegative, x4 + x2 + 1 ≠ −1, so x4 + x2 + 1 = 1. It follows that x4 + x2 = 0 and x = 0; SUFFICIENT.
If x3 + x2 = 0, then x2(x + 1) = 0. It follows that x = 0 or x = −1; NOT sufficient.
The correct answer is A;statement 1 alone is sufficient.
If x4 + x2 + 1 =
, then is its own reciprocal. The only numbers that are their own reciprocals are −1 and 1. Since even powers of x are nonnegative, x4 + x2 + 1 ≠ −1, so x4 + x2 + 1 = 1. It follows that x4 + x2 = 0 and x = 0; SUFFICIENT.
If x3 + x2 = 0, then x2(x + 1) = 0. It follows that x = 0 or x = −1; NOT sufficient.The correct answer is A;statement 1 alone is sufficient.
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