Extreme problems of weight approximation on the real axis

The exact value was calculated and the polynomial for the best weighted polynomial approximation was found for the kernels of the form \(\frac{A+Bx}{{({x}^{2}+{\uplambda }^{2})}^{2}}\) $\frac{A+Bx}{{(x^2+{\mathrm{\lambda }}^2)}^2}$ , where A,B ∈ \({\mathbb{R}}\) $\mathbb{R}$ and λ > 0, in the root-mean-square metric.