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  3. What is the value of x ? (1) x4 + x2+1 = (2) x3+x2 = 0

What is the value of x ? (1) x4 + x2+1 = (2) x3+x2 = 0

admin2022-10-18  48
问题 What is the value of x ?
(1) x4 + x2+1 =
(2) x3+x2 = 0
选项 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.
答案A
解析 (1)     If x4 + x2 + 1 = 1/(x4+x2+1)then x4+x2+1 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≠-l, so x4 + x2+l = 1. It follows that x 4 + x 2 = 0 and x = 0; SUFFICIENT.
(2)     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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