Solve for Reals

Solve for reals (x,y)

2^{y-x}(x+y)=1

(x+y)^{x-y}=2

8 Answers

62
Lokesh Verma ·

is this your doubt soumik?

1
arpan sinha ·

you can use gadha- ghora method of substitutinng
the options & check if they satisfy both!!: ;)

19
Debotosh.. ·

yup..i did just that ! there was no time to be a good mathematician at that stage ! [3]

11
Devil ·

So did I....Deobotosh.
But I wanna see if there's any general way without consulting the options....I cud not find any in the exam hall...
U can call this my doubt Nishant bhaiya.

1
akari ·

11
swaraj jena ·

2y-x(x+y)=1
=>x+y=2x-y
puting this value in another equation( 2x-y)x-y=2(x-y)2=2
=>(x-y)2=1
=>x-y=1
=>x=y+1
now puting the value of x in 1st eqn 2-1[y+1 + y]=1
=>2-1(2y+1)=1
=>y=1/2
=>x=3/2
now for x-y=-1
=>x=y-1
now puting the value of x in 1st eqn 21[y-1 + y]=1
=>21(2y-1)=1
=>y=3/4
=>x=-1/4

11
Devil ·

There's another ans.....
I guess that comes when (x-y)=-1.
DAMN I MISSED IT - IDIOTIC OF ME!!!

11
swaraj jena ·

arre bhaiya, my above two solns satisfy both the equation .so i think it should be the answer.

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