Solve This & Feel Like A Genius

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#math #brithemathguy #algebra

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[BriTheMathGuy]

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[zhiychen]

If you can't figure out adding +1 on your own, here's a geometric way.
1. Draw an x*y rectangle
2. Draw an 1*x rectangle below the x*y rectangle
3. Draw an y*1 rectangle on the left of the x*y rectangle
4. You will find that if you draw an 1*1 square below the y*1 rectangle, you get a (x+1)*(y+1) rectangle .
5. Therefore, you can write (x+1)(y+1)=xy+y+x+1=98+1.
6. Then you get (x+1)(y+1)=99, which has infinitely many solutions. For example, one of the solutions is x=10, y=8.

[rostfrst]

btw here are all the solutions for x and y are integers:
x=-100, y=-2
x=-34, y=-4
x=-12, y=-10
x=-10, y=-12
x=-4, y=-34
x=-2, y=-100
x=0, y=98
x=2, y=32
x=8, y=10
x=10, y=8
x=32, y=2

[smashliek]

this factoring method is called SFFT ( simon's favourite factoring trick)

[_lightless]

my thought process
x+xy+y=98
(x+1)y + x = 98
put in the second x anyway,
(x+1)(y+1)
this will leave a difference of exactly 1
(x+1)(y+1) - 1 = 98
(x+1)(y+1) = 99
x = 8
y = 10

[Devjeet]

I have solved these types of question in basic maths and I came to know that this method is known as Simon's factorizing technique.

[tylosenpai]

Simply put :
- Find the max to determine the maximum permitted values
- Accidentally find a solution

[Tryhad]

It was easier because my cram school textbook had a questions similar to this

[nicholasng]

Ah Simon's Favourite Factoring Trick, the factoring method that has saved me countless times.\

[mathyyys]

you can go with quadratic formulas and solve for non integers, i find it very beautiful

[shwetankupadhyay]

If it was not strictly based on positive integers then a simpler way to solve it is x+xy+y=98
y+y/x=98/x(deviding the equation by x)
xy+y/x=98/x
y(x+1)/x=98/x
y(x+1)=98
yx+y=98
yx=98-y
Now using the value of yx or xy in first equation
x+(98-y)+y=98
x=0 y=98

[arhaanshjhingan]

Bruh I saw the thumbnail used the same method mentally and got the answer in like 15 seconds

[DavidPumpernickel]

Anything nonlinear always feels great to solve

[aryamanjha]

we are not genius, I solved in thumbnail itself

[BloxxingDinosaurus]

x is 8, y is 10.
Or the other way around.

[Calculusgoat]

In the calculation in the first minute or two x=y in the equation x+xy+y=98

[Simpliriverr]

I love how I got it really easy and just stared at the thumbnail and ended up using a different method-

[Orange-xg]

Seprate out one variable in terms of other then you can easily see at what integer values of one variable, is the other one integer

x=(98-y)/(y+1)

[photon]

I did way less calculation in my head to get the same solutions

[Ostup_Burtik]

Plz, explain tetration for non-integer or imaginary, we really need this! And what is i^^i?