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Algebra Level 2

Let x x and y y be positive numbers satisfying x y = y x x^y = y^x and x = 2 y x= 2y , find the values of the pair ( x , y ) (x,y) .

( 4 , 2 ) (4,2) ( 8 , 4 ) (8,4) ( 6 , 3 ) (6,3) ( 2 , 1 ) (2,1)

Md Firoz Iqbal by MD FIROZ iQBAL , 26, Bangladesh

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2 solutions

Md Firoz Iqbal
Sep 1, 2016

5 Helpful 0 Interesting 0 Brilliant 0 Confused

2^y=y^y implies y=+-2. One more pair exists

Prince Loomba - 4 years, 9 months ago

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Totally right. So question has to be adapter or an answer adder.

Peter van der Linden - 4 years, 9 months ago

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Yes right but since its a MCQ I have no doubt in answer and got right haha

Prince Loomba - 4 years, 9 months ago

No,2^y=y^y does not implies that y=-2 as if we put the values in the equation then L.H.S becomes 1/4 and R.H.S becomes -1/4. So there is only one possibility that y=2

Satwik Murarka - 4 years, 9 months ago

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Do you know -1^even is 1? Both are equal

Prince Loomba - 4 years, 9 months ago

There are two solutions. ( − 4 , − 2 ) (-4,-2) and ( 4 , 2 ) (4,2) . Question should have been stated as "which of the following options .."

1 Helpful 0 Interesting 0 Brilliant 0 Confused

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