Question

If x=√5+√3/√5-√3 and y=√5-√3/√5+√3 then find x+y+xy

Answer 1

x= 8 + 2√15 / 2 = 4 + √15
y = 8 - 2√15 / 2 = 4 - √15

x+y = 8

xy = 16-15 = 1

x+y+xy = 8+1 = 9

Answer 2

Answer:

x + y + xy = 9

Step-by-step explanation:

If x = $\frac{(\sqrt{5}+\sqrt{3)}}{(\sqrt{5}-\sqrt{3)}}$ and y = $\frac{(\sqrt{5}-\sqrt{3)}}{(\sqrt{5}+\sqrt{3)}}$

Then (x + y) = $\frac{(\sqrt{5}+\sqrt{3)}}{(\sqrt{5}-\sqrt{3)}}+\frac{(\sqrt{5}-\sqrt{3)}}{(\sqrt{5}+\sqrt{3)}}$

                   = $\frac{(\sqrt{5}+\sqrt{3})^{2} +(\sqrt{5}-\sqrt{3})^{2} }{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$

                   = $\frac{5+3+2\sqrt{15}+5+3-2\sqrt{15}}{5-3}$  [Since (a + b)(a - b) = a² - b²]

                   = $\frac{16}{2}=8$

Similarly, xy = $\frac{(\sqrt{5}+\sqrt{3)}}{(\sqrt{5}-\sqrt{3)}}\times \frac{(\sqrt{5}-\sqrt{3)}}{(\sqrt{5}+\sqrt{3)}}$

                    = $\frac{(5-3)}{(5-3)}=1$

Now x + y + xy = 8 + 1

                        = 9

Therefore, (x + y + xy) = 9

Learn more, how to solve the fractions with complex numbers from https://brainly.in/question/8014721