Question

докажите числовое неравенство
даю 40 баллов​

Answer 1

$\displaystyle(\sqrt{5})^{log_5(\sqrt{2}-1)^2}+(\sqrt{3})^{log_3(\sqrt{2}-2)^2}=\\\\=(5^{\frac{1}{2}})^{2log_5|\sqrt{2}-1|}+(3^{\frac{1}{2}}^{2log_3|\sqrt{2}-2|}=5^{log_5|\sqrt{2}-1|}+3^{log_3|\sqrt{2}-2|}=\\\\=|\sqrt{2}-1|+|\sqrt{2}-2|=\sqrt{2}-1+2-\sqrt{2}=1$

равенство доказано