Question

If 72^x×48^y= 6^xy, x& y are non-zero rational numbers, then find x+y. Steps plz.​

Answer 1

Step-by-step explanation:

72

x

⋅48

y

=6

xy

⇒(2

3

⋅3

2

)

x

⋅(2

4

⋅3)

y

=2

xy

⋅3

xy

Equating powers of 2 and 3, we get

⇒3x+4y=xy…eqn(1)

⇒2x+3y=xy…eqn(2)

Subtract eqn(1) from eqn(2), we get

x=−3y Put this value of x in eqn (2).

−6y+y=−3y

2

⇒y=

3

5

and x=−5

x+y=−5+

3

5

=

3

−10