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If x, y are rational numbers such that (...

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

A

`x=1,y=1`

B

`x=2,y=1`

C

`x=5,y=1`

D

x & y can take infinitely many values

Text Solution

AI Generated Solution

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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  • If x,y are rational numbers and (5+sqrt(11))/(3-2sqrt(11))=x+ysqrt(11) . The values of x and y are

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