Question

Suppose that the number of elements in the set $S$ is $105$ and that $S$ is split into $m$ subsets $11m+2$ elements each. If $m$ is an integer, then $m$ is

Answer 1

Given that

$\Rightarrow m(11m+2)=105$

$\Rightarrow 11m^2+2m-105=0$

Using the formula $\Rightarrow x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ we get

$\Rightarrow m=\frac{-2\pm \sqrt{2^2-4\left(11\right)(-105)}}{2\times 11}$

$\Rightarrow m=\frac{-2\pm \sqrt{4+4620}}{22}$

$\Rightarrow m=\frac{-2\pm \sqrt{4624}}{22}$

$\Rightarrow m=\frac{-2\pm 68}{22}$

$\Rightarrow m=\frac{-2+68}{22}andm=\frac{-2-68}{22}$

$\Rightarrow m=\frac{66}{22}andm=\frac{-70}{22}$

$\Rightarrow m=3andm=\frac{-70}{22}$

Given that $m$ is an integer.

Hence, $m=3$