The Number Of Solutions Of `3^{X+Y}` = 243 And `243^{X-Y}` = 3 Is - Mathematics

The number of solutions of `3^{x+y}` = 243 and `243^{x-y}` = 3 is 

(a) 0 

(b) 1 

(c) 2 

(d) infinite




(b) 1 

Explanation:

= `3^{x+y}` = 243

= `3^{x+y}` = `3^{5}`

= x + y = 5 -----------------(i)

= `(243)^{x-y}` =3

= `(3^{5})^{x-y} =3^{1}`

So,

= 5x -5y =1 -------------(ii)

Since, `\frac{a_{1}}{a_{2}}\ne\frac{b_{1}}{b_{2}} `

Since, Only one Pair of solution are there

∴ Number of Solution = 1







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