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
0 تعليقات