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x-y-y-x-x-2-y-3-find-x-and-y-




Question Number 11805 by tawa last updated on 01/Apr/17
x^y  = y^x       x^2  = y^3   find x and y
xy=yxx2=y3findxandy
Answered by mrW1 last updated on 01/Apr/17
(i)⇒x=y^(x/y)   (ii)⇒x=y^(3/2)   ⇒(x/y)=(3/2)  ⇒x=(3/2)y  (3/2)y=y^(3/2)   (3/2)=y^(1/2)   ⇒y=((3/2))^2 =(9/4)  ⇒x=(3/2)×(9/4)=((27)/8)
(i)x=yxy(ii)x=y32xy=32x=32y32y=y3232=y12y=(32)2=94x=32×94=278
Commented by tawa last updated on 01/Apr/17
wow, God bless you sir.
wow,Godblessyousir.
Commented by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17
x=y=1 also is an answer.
x=y=1alsoisananswer.
Commented by mrW1 last updated on 01/Apr/17
that′s right.
thatsright.
Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 01/Apr/17
x^(2y) =y^(2x) ⇒(x^2 )^y =y^(2x) ⇒(y^3 )^y =y^(2x)   3y=2x⇒((3/2)y)^2 =y^3 ⇒9y^2 =4y^3 ⇒  y^2 (4y−9)=0⇒y=(9/4)⇒x=(3/2)×(9/4)=((27)/8)
x2y=y2x(x2)y=y2x(y3)y=y2x3y=2x(32y)2=y39y2=4y3y2(4y9)=0y=94x=32×94=278

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