Atrisinājums

Atbilde: \(a=1\).

1) ja \(x>y>1\), tad \(x-1>y-1>0\), tāpēc \((x-1)^{2}>(y-1)^{2}\), no kā seko \(x^{2}-2x>y^{2}-2y\). 2) ja \(0<a<1\), tad eksistē tādi \(x_{1}\) un \(x_{2}\), ka \(0<a<x_{1}<1<x_{2}\) un \(\left(x_{1}-1\right)^{2}>\left(x_{2}-1\right)^{2}\), skat. zīm.