Question

solve the following pair of equation : 2/root x +3/root y =2 and 4/ root x -9/root y =-1

Answer 1

first given equation

2/√ x +3/√y = 2

3√x + 2√y /√xy =2

3√x + 2√y / 2 = √xy -------( 1 )


second given equation

4/ √x -9/√y = -1

-9√x + 4√y / √xy = -1

-9√x + 4√y / -1 = √xy

9√x - 4√y = √xy -------- ( 2 )

from 1 and 2

3√x + 2√y / 2 = 9√x - 4√y

3√x + 2√y = 18√x - 8√y

18√x - 3√x = 8√y + 2√y

15√x = 10√y

√x / √y = 10 / 15

√x / √y = 2/3

squaring both sides

x / y = 4 /9