if x=3/4-3/4-x then one value of x is
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Answer:
By trial, x=2 is a root of the equation . Dividing the equation by 5
x
we get
(
5
3
)
x
+(
5
4
)
x
=1
If x<2, then (3/5)
x
>(3/5)
2
and (4/5)
x
>(4/5)
2
and so on
(3/5)
x
+(4/5)
x
>(3/5)
2
+(4/5)
2
=1
Hence (1) is not satisfied for any value of x<2.
Similarly, for x>2, we will always have the inequality (3/5)
x
+(4/5)
x
<1
Thus x=2 is the only root of the given equation. Note that it is immaterial how we found a root, but it is necessary to show that there are no other roots.
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