Question

if x= √2+1/√2-1 and y = √ 2-1/√2+1. find x2+ y2 + xy

Answer 1

jus rationalize the denominator and you will get the ans

you can also directly put the value of x and y (after rationalizing) in the equation x2+y2+xy

.....hope this helps..☺

Answer 2

Answer:

$x^2+y^2+xy=35$

Step-by-step explanation:

Given : $x=\frac{\sqrt2+1}{\sqrt2-1}$ and $y=\frac{\sqrt2-1}{\sqrt2+1}$

To find : The value of $x^2+y^2+xy$

Solution :

First we solve the value of x and y be rationalizing,

The value of x,

$x=\frac{\sqrt2+1}{\sqrt2-1}$

$x=\frac{\sqrt2+1}{\sqrt2-1}\times\frac{\sqrt2+1}{\sqrt2+1}$

$x=\frac{(\sqrt2+1)^2}{(\sqrt2)^2-1^2}$

$x=\frac{2+1+2\sqrt2}{2-1}$

$x=3+2\sqrt2$

The value of y,

$y=\frac{\sqrt2-1}{\sqrt2+1}$

$y=\frac{\sqrt2-1}{\sqrt2+1}\times\frac{\sqrt2-1}{\sqrt2-1}$

$y=\frac{(\sqrt2-1)^2}{(\sqrt2)^2-1^2}$

$y=\frac{2+1-2\sqrt2}{2-1}$

$y=3-2\sqrt2$

Now, Substitute the value of x and y in the expression

$x^2+y^2+xy$

$=(3+2\sqrt2)^2+(3-2\sqrt2)^2+(3+2\sqrt2)(3-2\sqrt2)$

$=9+8+12\sqrt2+9+8-12\sqrt2+3^2-(2\sqrt2)^2$

$=17+17+9-8$

$=35$

Therefore, $x^2+y^2+xy=35$