Question

(e^x)+(3e^y)=3 and (e^2x)-(9e^2y)=6
find the values of x and Y.
some please help me out!!

Answer 1

If e^x=u and e^y=v.
Then u+3v=3. and u^2-9v^2=6.
Using a^2-b^2=(a+b)(a-b)
(u+3v)(u-3v)=6
u+3v=3.
so u-3v=2.
and u+3v=3.solve these two.

Answer 2

thank you very much :D

Answer 3

\[e ^{2x}-9e ^{2y}=(e ^{x}-3e ^{y})(e ^{x}+3e ^{y})=6\]

Answer 4

But e^x+3e^y=3 so substitute.

Answer 5

\[(e ^{x}-3e ^{y})(3)=6\]

Answer 6

\[e ^x-3e ^{y}=2\]

Answer 7

But from the first equation
\[e^x+3e^y=3\]

Answer 8

Add those two equations.

Answer 9

\[2e^x=5, e^x=\frac{5}{2}\]

Answer 10

\[x=\ln (\frac{5}{2})\]

Answer 11

\[ y = \ln\frac{1}{6}\]

Answer 12

Forgot to say that.