Question

if x=2/√3-√5and y=2/√3+√5,then x+y​

Answer 1

Step-by-step explanation:

We know that,

(x + y)(x - y) = x² - y²

Therefore,

$\begin{gathered} x^2 - y^2 = (\frac{2 - \sqrt{5}}{2 + \sqrt{5}} + \frac{2 + \sqrt{5}}{2 - \sqrt{5}})(\frac{2 - \sqrt{5}}{2 + \sqrt{5}} - \frac{2 + \sqrt{5}}{2 - \sqrt{5}}) \\ \\ = (\frac{(2 - \sqrt{5})^2 + (2 + \sqrt{5})^2}{(2 + \sqrt{5})(2 - \sqrt{5})})(\frac{(2 - \sqrt{5})^2 - (2 + \sqrt{5})^2}{(2 + \sqrt{5})(2 - \sqrt{5})}) \\ \\ = (\frac{9 - 4\sqrt{5} + 9 + 4\sqrt{5}}{4 - 5})(\frac{9 - 4\sqrt{5} - 9 - 4\sqrt{5}}{4 - 5}) \\ \\ = \frac{18}{- 1} \times \frac{- 8\sqrt{5}}{- 1} = \frac{- 144\sqrt{5}}{1} = - 144\sqrt{5} \end{gathered}$

- 144√5 is the answer.

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Answer 2

Answer:

2−

5

2+

5

=

2−

5

2+

5

×

2+

5

2+

5

=

2 2

5

) 2

(2+

5

) 2

=

4−5

4+4

5

+5

=

−1

9+4

5

=−9−4

5

(−9−4

5

) 2

5

) 2

=81+72

5

+80−(81−72

5

+80)

=81+72

5

+80−81+72

5

−80

=144

5

=

2+

2−

=

=