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Question Number 33766 by .none. last updated on 23/Apr/18

$$a-\frac{1}{a}=4$$$$\sqrt{a^2+\frac{1}{a^2}}-\sqrt{{(a+\frac{1}{a})}^2}-\sqrt{{(a-2)}^2}=\sqrt{x}-\sqrt{y}$$$$whatis[x+y]?$$

Answered by MJS last updated on 23/Apr/18

$$a=2\pm \sqrt{5}$$$$\sqrt{a^2+\frac{1}{a^2}}=3\sqrt{2}$$$$\sqrt{{(a+\frac{1}{a})}^2}=2\sqrt{5}$$$$\sqrt{{(a-2)}^2}=\sqrt{5}$$$$3\sqrt{2}-2\sqrt{5}-\sqrt{5}=\sqrt{x}-\sqrt{y}$$$$3\sqrt{2}-3\sqrt{5}=\sqrt{x}-\sqrt{y}$$$$\sqrt{18}-\sqrt{45}=\sqrt{x}-\sqrt{y}$$$$x=18$$$$y=45$$$$x+y=63$$

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