Question

if x is equal to root 5 + root 3 by root 5 minus root 3 and Y is equal to root 5 minus root 3 by root 5 + root 3 then find X + Y + xy

Answer 1

I think it must be helpful ...

Answer 2

Answer:

The value of X + Y + xy = 9.

Step-by-step explanation:

Given:

$x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \cdot \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

To find:

the value of X + Y + xy

Step 1

Let the equation x be

$x=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} \cdot \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}}$

Simplifying the above equation, we get

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

$=\frac{8+2 \sqrt{15}}{2}$

Step 2

Let the equation y be

$y=\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}+\sqrt{3}} \cdot \frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$

Simplifying the above equation, we get

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

$=\frac{8-2 \sqrt{15}}{2}$

Step 3

Therefore, by multiplying both of the above equations, we get

$x y=\left(\frac{8+2 \sqrt{15}}{2}\right)\left(\frac{8-2 \sqrt{15}}{2}\right)$

$=\frac{64-(2 \sqrt{15})^{2}}{4}=\frac{64-60}{4}=1$

Therefore, xy = 1.

Step 4

$x+y+x=\frac{8+2 \sqrt{15}}{2}+\frac{8-2 \sqrt{15}}{2}$

$=\frac{8+2 \sqrt{15}+8-2 \sqrt{15}}{2}$

$=\frac{16}{2}=8$

$x+y+x y=8+1=9$

Therefore, the value of X + Y + xy = 9.

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