Hi,
Someone give me a hand in checking these please.
a.) Given that, and
for the real numbers
,
and
, show that
.
...1
is +ve...2
...3
Ifthen
is +ve
Putting values using lines 2 and 3
OR
...................OR
+ve
therefore
b.) Show that if x, y ∈ R, and, then for any real number
...1
is -ve
Ifthen
is -ve
Putting in values using lines 2 and 3
................OR
)
thereforemust be true
If x = 3, y = 2, and k = -1, then kx = -3, which is less than y. So your last line above cannot be assumed always to be true.Originally Posted by Hellbent
a.) Given that
Try starting like this:
Let x > y, and let k < 0. Assume that kx > ky. Then kx - ky > 0. Also, kx - ky = k(x - y). Since x > y, then x - y > 0.
See where this leads....
Am I right this time?
a.) Since x > y, so x - y is positive and k is negative.
Product of a negative and positive number is negative, kx - ky
Hence it follows that kx < ky.
b.) Since x < y, so x - y is negative and k is negative.
Product of two negative numbers is equal to a positive number.
Hence it follows that kx > ky.
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