If x, y are rational numbers such that `(x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5)` then

Options

A. `x=1,y=1`
B. `x=2,y=1`
C. `x=5,y=1`
D. x & y can take infinitely many values

Explanation

To solve the equation \((x+y) + (x-2y)\sqrt{2} = 2x - y + (x-y-1)\sqrt{5}\), we will separate the rational and irrational parts and equate them.

### Step 1: Identify Rational and Irrational Parts
We can rewrite the equation as:
- Left-hand side (LHS): \( (x+y) + (x-2y)\sqrt{2} \)
- Right-hand side (RHS): \( (2x - y) + (x-y-1)\sqrt{5} \)

### Step 2: Equate Rational Parts
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