Question

. If x = 2, y=-3, find the value of :
(1) x^x + y^y
(11) x^y + y^x
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Answer 1

Answer:

Answer

Put x+y=u and xy=v. Then the given equations can be written as

u+v=11,uv=30

∴ u and v are the roots of t

2

=11t+30=0

Hence u=6,v=5 or u=5,v=6.

Thus x+y=6,xy=5 or x+y=5,xy=6

First we take x+y=6 ..(1)

and xy=5

∴ x and y are the roots of t

−

6t+5=0

or (t−5)(t−1)=0,

∴t=5,1

Hence x=5,y=1 or x=1,y=5.

We now take x+y=5,xy=6.

Solving these, we shall get t

2

−5t+6=0

x=3,y=2 or x=2,y=3

Hence the solution set is (5,1),(1,5).(3,2),(2,3).

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