Absolutely

Algebra Level 5

For all real k k , let

S k = k k 2 × k 2 k S_{k}=|\frac {k}{k^{2}}|×|\frac {k^{2}}{k}|

Which of the following must be true?

S k = 1 S_{k}=1 or 1 -1 S k = k S_{k}=-k S k = 1 S_{k}=-1 None of the rest S k = 1 S_{k}=1 S k = k S_{k}=k or k -k S k = k S_{k}=k

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2 solutions

Joel Tan
Apr 21, 2015

S 0 S_{0} is undefined.

For those who did not solve it: consider all cases regardless of the difficulty of the problem.

So, we have, by the identity a b = a b |a|\cdot |b|=|ab| that,

S k = 1 k R { 0 } S_k=1~\forall~k\in\Bbb{R}\setminus\{0\}

Prasun Biswas - 6 years ago
Aayush Patni
Apr 21, 2015

K can be zero also. 0/0 is not defined. Therefore none of these

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