Question

Find x and y when 1/4 + √11 = x - y √11

Answer 1

Answer:

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}