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# Need Help!

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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
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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 . . . ^^ !

Nov 11, 2021
#2
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Is the expression on the right supposed to be (ab)2  or  a • b2   ?

Nov 12, 2021
#3
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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
+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

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yea I don't know.

There are at least 2 answers. Nov 17, 2021