Question

math for KIDS :P

Answer 1

Much more like math for adults.

Answer 2

I don't know... gah

Answer 3

Looks like I'm still a toddler.

Answer 4

*

Answer 5

Why many of us still feel like a kid?

Answer 6

whoa thats a long problem

Answer 7

my first guess is to play with

\[17\mid a ~~\text{and}~~17\mid b \implies 17\mid(ma\pm nb)\]

Answer 8

\[\left[ \begin{array}c 1 & -3/2\\-3/2 & 2\\\end{array} \right]\] and \[\left[ \begin{array}c 0 & 1/2\\1/2 & 0\\\end{array} \right]\] have the same determinant

Answer 9

\(\large \color{black}{\begin{align}
x^2-3xy+2y^2+x-y=17m\hspace{.33em}\\~\\
(x-2y+1)(x-y)=17m\hspace{.33em}\\~\\
\end{align}}\)

we can consider here
4 cases


\(\large \color{black}{\begin{align}
x-2y+1=17,\ x-y=m \hspace{.33em}\\~\\
x-2y+1=m,\ x-y=17 \hspace{.33em}\\~\\
x-2y+1=17m,\ x-y=1 \hspace{.33em}\\~\\
x-2y+1=1,\ x-y=17m \hspace{.33em}\\~\\
\end{align}}\)

Answer 10

@mathmath333 How did you factor that, I wanna learn how you figured that out.

Answer 11

do u agree m should be an integer

Answer 12

Ahh nice, factoring the quadratic \(x^2-3xy+2y^2\) is easy using factor by grouping :

\[x^2-3xy+2y^2 = x^2-xy-2xy+2y^2 = x(x-y)-2y(x-y)\]

Answer 13

a bit enlightening to notice that any quadratic equation of form \(ax^2+bxy+cy^2=0\) represents a pair of straight lines passing thru origin and thus can be factored as \((y+m_1x)(y+m_2x)=0\)

Answer 14

Ahhh ok thanks @ganeshie8 I worked through a few but I like the fact that all equations of that form in n variables seems to imply that it's really n lines through the origin, interesting.

Answer 15

well done guys. heres the solution -

Answer 16

i wonder if i played with the linear combination, how it would end nicely

Answer 17

that is also neat

Answer 18

I tried to see if the final one was a linear combination of the two but it doesn't appear to be, try subtracting one from the other to get rid of the x^2 but you'll still have the y^2 that you can't get rid of @ikram002p

Answer 19

well yeah (there is no linear combination ) see why :-
m x^2-2mxy+my^2-5mx+7my
nx^2-3nxy+2ny^2+nx-ny
-------------------------
xy -12x+15y

set of equations:-
m=n
2n=m
-2m-3n=1
-5m+n=-12
7m-n=15