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Mathematica can't solve simple system of equations


Assume I have two equations a[i]^x(a[i]^x+a[j]^x)^(1/x)-p[i], where
i=1,2, i!=j (not equal), and all variables, {a,x,p} are strictly
positive. Mathematica cannot  give me the answer that I can work out by
hand in less than a minute. I used both Solve and Reduce to solve for
a[i], i=1,2. Please advise. Mukhtar Bekkali


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