Question

if x, y are rational numbers such that (x + y) + (x - 2y) √2 = 2x - y + ( x - y - 1 )√5 then find the values of x and y

Answer 1

To solve this Question, A Property is to be kept in mind
The product of a non-zero rational number and an irrational number is irrational.
The Product of zero and an irrational number is zero.

Now as shown in the image attached.

In the Third step we get,

(x - 2y)×${ \sqrt{2} -1/ \sqrt{5} }$ = x-y-1



Now, RHS is clearly Rational as x,y,1 are all rational


for the equality, LHS should also be Rational but the first part of equality i.e. x-2y is rational while the other part is irrational
Now, for the product of first part and Second part to be rational (x-2y) should be zero and altogether LHS should be zero.


So, We get  two equations
                  x-2y=0    ...........(1)
                 x-y-1=0    ...........(2)

solving (1) and (2), we get

                  x=2      y=1

Answer 2

Answer:

x=2.y=1

Step-by-step explanation:

hope so my answer helps you