If |b| ≥ 1 and x= -| a| b, then which one of the following is necessarily true?
Choose the correct choice from the following options:
A) a -xb < 0  B) a -xb ≥ 0  C) a -xb > 0  D) a -xb ≤ 0  E) None of these
Explanation :   x = –|a| b   Now a – xb = a – (– |a| b) b   = a + |a| b2   ∴ a – xb = a + ab2 … a 0 ≥ OR a – xb   = a - ab2 …a &lt; 0   = a(1 + b2) = a(1 – b2).   Consider first case:   As a ≥ 0 and |b| ≥ 1, therefore (1 + b2) is positive.   ∴ a (1 + b2) ≥ 0   ∴ a – xb ≥ 0   Consider second case.   As a &lt; 0 and |b| ≥ 1, therefore (1 – b2) ≤ 0   ∴ a (1 – b2) ≥ 0 (Since –ve × -ve = +ve and 1 – b2 can be zero also), i.e. a – xb ≥ 0   Therefore, in both cases a – xb ≥ 0.   Answer : a -xb ≥ 0
<result>B</result>
If |b| ≥ 1 and x= -| a| b, then which one of the following is necessarily true?