IMO 1985 LL CYP19

Origin: CYP

Problem

Solve the system of simultaneous equations \sqrtx −1/y − 2w + 3z = 1, x + 1/y2 −4w2 −9z2 = 3, x\sqrtx −1/y3 −8w3 + 27z3 = −5, x2 + 1/y4 −16w4 −81z4 = 15.