olymmath

KöMaL 2021 B5178

    Let xx be a positive real number. Show that 6x+9+16x+64≤(x+3x)(x+8x).\sqrt{6x+9}+\sqrt{16x+64}\le \left(\sqrt{x}+\frac{3}{\sqrt{x}}\right) \left(\sqrt{x}+\frac{8}{\sqrt{x}}\right).

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