Oxford University MAT 2019 Solved Papers

Question : 9 of 10

Marks: +1, -0

The positive real numbers

x

and

y

satisfy

0< x< y

and
$ x 2^x=y 2^y .
$
for

Solution:

Both

x

and

2^x

are strictly increasing for

x>0

, so their product is strictly increasing.

x 2^x

therefore takes no values twice for

x>0

, so there are no solutions to the given equation with

0< x< y

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