Doesn't matter what it means!

Algebra Level 3

Define $/x/$ as the $\textbf{anti-modulus}$ of $x$ ,behaving exactly opposite from that of $\text{modulus}$ of x.[for example, if we take $x={5,-5}$ then, l5l=l-5l=5, but $/5/=/-5/=-5$ . Also, I0I= $/0/$ =0].

Also define $\text{Mil(y)={8 million+(3 million times y)}}$ .

What is the divisibility status of $\text{Mil(sum of roots of the equation}$ $(/x/)^{2}-4x+3=0$ ) by $16?$

not divisible can't be determined (/x/)^2-4x+3=0 has no root in any system of numbers divisible

1 solution

Anandmay Patel
Jul 28, 2016

$\text{By experimenting,we find the 'key to solution' of this question,i.e.,}$ $(/x/)^2=x^2$ . $\text{So the sum of roots of the equation}$ $(/x/)^2-4x+3=0$ $\text{is 4 as the sum of roots of the equation}$ $x^2-4x+3=0$ $\text{is}$ $4$ . $\text{Now by simple arithmetic work, we can prove its divisibility by}$ $16$ .

Is modulus the same as absolute?

William Nathanael Supriadi - 4 years, 6 months ago

Yes you are right.The modulus of a number means its absolute value.

Anandmay Patel - 4 years, 6 months ago

Doesn't matter what it means!

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