How many integer solutions for (a, b) satisfied the following equation

a^2+b^2=ab^2

Guest Nov 11, 2021

#1**+1 **

Hello Guest,

How many integer solutions for (a, b) satisfied the following equation

a^2+b^2=ab^2

\(a^2+b^2=ab^2\)

\((a, \mbox { } b) = (2, \mbox {} \pm \mbox { } 2) \)

\((a, \mbox { } b) = ( \pm \mbox { } 2, \mbox { } 2)\)

\((a, \mbox { } b) = (0, \mbox { } 0)\)

Hope this was helpful . . . ^^

!

Straight Nov 11, 2021

#4**+1 **

Fist thing I did was graph it.

https://www.geogebra.org/classic/svfrstbf

a^2+b^2=ab^2

its symetrical so I want to look at the top half b>0 (then I will double the number of answers)

\(a^2=ab^2-b^2\\ a^2=b^2(a-1)\\ b=\frac{a}{\sqrt{a-1}} \)

a has to be greater than 1,

For b to be an integer

a^2 = k (a-1) where k is an integer

---------------------------------

yea I don't know.

There are at least 2 answers.

Melody Nov 17, 2021