1WELL GOVIND ANS=0 AND 10
ie x=y=0
put x2=y....in the other eqn
u get y=2x
take log on both sides of 1st eqn and sustitute the value
of y=2x
if xy=yx and x2=y, where x and y are dinstinct positive real integers then the value of of x+2y is
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UP 0 DOWN 0 0 3
3 Answers
29well just at looking at the question the first thing that came to my mind..
is that the numbers can be 2 and 4 ...since 24 = 42 and moreover it satisfy the other condition too 22 = 4
so x = 2 and y = 4..
value of x + 2y = 10..
sry but i dunno the right method to do it...will be good if someone posts it...
1
11xy = yx
Taking log on both sides...
y log x = x log y .....(1)
next x2 = y
Taking log on both sides..
2 log x = log y...(2)
dividing (1) & (2)..
y log x = x log y2 log x = log y.
solving we get y = 2x
substituting in (2)..
2 log x = log (2x)
2 log x = log 2 + log x
log x = log 2
x = 2
=> y = 4..
so x+2y = 2+2(4) = 10...
and yup as 0 is also possible....
so answers are 0 and 10...