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Question Number 161061 by cortano last updated on 11/Dec/21

Answered by MJS_new last updated on 11/Dec/21

$$\sqrt{A}-\sqrt{B}=x\sqrt{C}$$$$A+B-2\sqrt{AB}=x^{2}C$$$$2(2^{3/4}-\sqrt{1+\sqrt{2}})=x^2(2^{3/4}-\sqrt{1+\sqrt{2}})$$$$x^2=2$$$$x=\sqrt{2}\mathrm{because}\mathrm{obviously}\sqrt{A}-\sqrt{B}>0$$

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