This is the third proof problem of the series "Olympiad Proof Problems". Try this problem and post your working.
Find the maximum value of the expression \(ab + bc + cd + da\), subject to the conditions \(abcd = 4\) and \(a^2 + b^2 + c^2 + d^2 =10\).
Details and Assumptions :
- \(a\), \(b\), \(c\) and \(d\) are positive real numbers
Try more proof problems at Olympiad Proof Problems.
EDIT: When dealing with inequalities, find out the condition of equality and check whether the equality condition satisfies the given constraints.