Question

if x = √2-1/√2+2 and y = √2+1/√2-1 find x + y​

Answer 1

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

Answer 2

Step-by-step explanation:

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