Question

write the three solutions of X + root 3 Y = 6

Answer 1

X=3 and y =root 3.x=6 and y=0.x=0 and y=2root3

Answer 2

x + √3 y = 6

√3 is irrational  and 6 is rational

We know that only irrational × irrational may be rational

So y must have √3 multiple.

Trial and error

x + √3 y = 6

Put y as √3

x + 3 = 6

==> x = 6 - 3

==> x = 3

Put y as 2√3

x + √3 × 2√3 = 6

==> x + 6 = 6

==> x = 0

Put y as -√3

x + √3 . -√3 = 6

==> x - 3 = 6

==> x = 9

From trial and error the answers are:

ANSWERS

x = 9 , y = -√3

x = 3 , y = √3

x = 0 , y = 2√3

Hope it helps :-)

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