a-1-a-4-a-2-1-a-2-a-1-a-2-a-2-2-x-y-what-is-x-y-

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}

w h a t i s [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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