Question

if 5+root 11 / 3-2 root 11 = x+y root 11 find the value of xand y

Answer 1

Hope it will help you

Answer 2

Answer:

x=$\frac{-37}{35}$ and y=$\frac{-13}{35}$

Step-by-step explanation:

Given: $\frac{5+\sqrt{11}}{3-2\sqrt{11}}$

Rationalise the above equation, we have

$x+y\sqrt{11}$=$\frac{5+\sqrt{11}}{3-2\sqrt{11}}{\times}\frac{3+2\sqrt{11}}{3+2\sqrt{11}}$

$x+y\sqrt{11}$=$\frac{15+3\sqrt{11}+10\sqrt{11}+22}{9-44}$

$x+y\sqrt{11}$=$\frac{37+13\sqrt{11}}{-35}$

$x+y\sqrt{11}$=$\frac{-37}{35}+\frac{-13}{35}\sqrt{11}$

Now, comparing the LHS and RHS,

x=$\frac{-37}{35}$ and y=$\frac{-13}{35}$