I got the abswer as (3,+infinite) but according to my book the answer is different.
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If you multiply both sides by x to get rid of the denominator, you need to take into account 2 cases, one where x > 0 (and the inequality will keep the same sign) and one where x < 0 (and the inequality will reverse its sign).
It doesn't.It has 2 roots.
Originally Posted by kastamonu x+1/3>=4/x
I got the abswer as (3,+infinite) but according to my book the answer is different. You can be pretty sure anything Prove It tells you is correct.
$x + \dfrac 1 3 \geq \dfrac 4 x$
if $x>0$ then
$x^2+\dfrac x 3 - 4 \geq 0$
but if $x<0$ then
$x^2+\dfrac x 3 -4 \leq 0$
you can go ahead and solve these under the 2 conditions
first one is (-inf.,-5/3) u (2/3,+inf.)
In the question it is asking how many natural numbers are there that satisfy this equation? By this solution it seems to be infinite.
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