If n denotes a number to the left of 0 on the number line such that the square of n is less than

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If n denotes a number to the left of 0 on the number line such that the square of n is less than

?f=%5Csmall%20%5Cfrac%7B1%7D%7B100%7D" id="TexFormula1" title="\small \frac{1}{100}" alt="\small \frac{1}{100}" align="absmiddle" class="latex-formula">, then the reciprocal of n must be _________.

Mathematics

1 answer:

Alex · Answer 1 · 2020-12-21T04:47:30+03:00

The reciprocal of n must be less than –10

Solution:

Given n denotes a number to the left of 0 means n < 0.

Square of n is less than $\frac{1}{100}$ means $n^2$ .

Therefore, we have $n$ and $n^2$ .

⇒ $n^2$

Taking square root on both sides, we get

⇒ $n$

⇒ $\frac{-1}{10}$

⇒ But we know that n < 0, so $n$ false.

It should be $\frac{-1}{10}$ .

To equal the expression, multiply both sides of the equation by –10n.

⇒ $-\frac{1}{10} \times\frac{-10}{n}>n \times\frac{-10}{n}$ (symbol < changed to > when multiply by minus)

⇒ $\frac{1}{n}>-10$

Hence, the reciprocal of n must be less than –10.