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

a^2+b^2=ab^2

 Nov 11, 2021
 #1
avatar+391 
+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 . . . ^^

 

smiley !

 Nov 11, 2021
 #2
avatar
+1

 

Is the expression on the right supposed to be (ab)2  or  a • b2   ?  

 Nov 12, 2021
 #3
avatar+391 
+1

Hello Guest,

 

\(\mathcal { \mbox {Is the expression on the right supposed to be (ab)²  or  a • b²   ? }}\)

 

In this case \(a^2+b^2=ab^2\) , whereby one can also rewrite this to \(a \cdot b^2\) .

 

Straight

Straight  Nov 12, 2021
 #4
avatar+115391 
+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.

 

 Nov 17, 2021

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