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With the rapid development of asteroseismology thanks to space-based photometry missions such as CoRoT, Kepler, TESS, and in the future, PLATO, and the use of inversion techniques, quasi-model-independent constraints on the stellar properties can be extracted from a given stellar oscillation spectrum. In this context, inversions based on frequency separation ratios, that are less sensitive to surface effects, appear as a promising technique to constrain the properties of stellar convective cores. We developed an inversion based on frequency separation ratios with the goal of damping the surface effects of the oscillation frequencies. Using this new inversion, we defined a new indicator to constrain the boundary mixing properties of convective cores in solar-like oscillators. We verified our inversion technique by conducting tests in a controlled environment, where the stellar mass and radius are known exactly, and conducted an extensive hare and hounds exercise. The inversion is not affected by surface effects. With the construction of an extensive set of models, favoured and forbidden regions can be highlighted in the parameter space. If the ratios are well fitted, the inversion is unsurprisingly not providing additional information. The indicator coupled with the inversion based on frequency separation ratios seems promising at probing the properties of convective cores, especially for F-type stars exhibiting solar-like oscillations.