IIT JEE , AIEEE Forum - Mathematics , Algebra - Solution to problem without trial and error

Marlin

X+Y=5

X^y+Y^X=17

Solve this without trial and error

aysh

i think graphs could b the best answer.

by the way,

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

dvrravi

i think you have to use logs for this one..
but trial and error seems to be a better option..

asurekha1970

X+Y=5

X^y+Y^X=17

Solve this without trial and error

take log to second equation then

ylogx+xlogy=log17dividing throught by xy then

ylogx\xy+xlogy\xy=log17\xy

logx\x+logy\y=log17\xy

integrating on both sides

_{[ ]}

^{[ ]} logx\xdx+_{[ ]}

^{[ ]} logy\ydy=_{[ ]}

^{[ ]} log17\xydxdy_{[ ]}

^{[ ]}

(logx)^2+(logy)^2=constant

asurekha1970

10 people do 1 work in 12 hours...
so 10 people do 1/4 work in 12/4 hours = 3 hours...
1 people will do in 10x3 hours = 30 hours
so 6 will do in 30/6 hours = 5 hours

asurekha1970

Q)value of cos^-1(cos 7

/6) is.............................

7*180/6=7*30=210degrees

vish0001

hey, i think trial and error method only work here !!!

puneet

hii

see this is a tuff one ..

it is very difficult to solve such question without hit n trial answer is 2,3 indeed

u can draw certain conclusions but this is a function in which u cannot solve ..

very difficult ..

hit n trial is the way .. in some cases some eqn may work but for sure not in all

cheers

Arjun

anasurekha ur wrong how can u take log!!!!!!!!!!!

Marlin

aysh you are rigtht about graphs the equations give two curves and a straight line passing through(2,3) & (3,2) but think something else there is other way round.Asurekha you cannot take log like that
however you can try this way

X^Y=C
Y^X=K

C+K=17
you can now take log.

A better solution to this problem is necessary.And any one dose that...................

vasanth

takin log for the second eq

y logx + x logy = log 17

(5-x)logx + x log(5-x) = log 17

5logx - xlogx - x(logx)/(log5) = log17

logx (5 - x - x/log5) = log 17

u can compute log5 and log 17 from the values of log2, log3

finally u'll arrive at the value of x in terms of logx

for solvin this u need to memorise the log table...........

so the best method is trial n eror method

cheeeeeers

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