Question

Se stie ca y√2+y√3=3.Atunci y este egal cu...
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Answer 1

    
[tex]\displaystyle y\sqrt{2}+y \sqrt{3}=3 \\ \\ y\sqrt{3}+y \sqrt{2}=3\\ \\ y(\sqrt{3}+\sqrt{2})=3 \\ \\ y= \frac{3}{\sqrt{3}+\sqrt{2}} = \\ \\ \\ =\frac{3(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})}= \\ \\ \\ =\frac{3(\sqrt{3}-\sqrt{2})}{(\sqrt{3})^2-(\sqrt{2})^2} = \frac{3(\sqrt{3}-\sqrt{2})}{3-2}=\boxed{3(\sqrt{3}-\sqrt{2})}[/tex]