Transforming an indirect utility function into an expenditure function in preparation for our upcoming exam, our tutor has uploaded sample questions. One of them is the following:



This is my solution:



Which differs from the solution, which gives the ordinary square root of the same parameters, not the 4th-one. I can't find my mistake, does anyone have any ideas?
There is no error in your calculations. The problem is with the indirect utility function that you were given. 

An indirect utility function should satisfy $v(\alpha p_1,\alpha p_2,\alpha y)=v(p_1,p_2,y)$. In other words, if income goes up and prices go up by the same factor then everyone is as well off as they were before.

Unfortunately, in this case $v(\alpha p_1, \alpha p_2, \alpha y)= \frac{1}2\alpha^2\frac{y^4}{p_1p_2}$