SOLUTION: t^2-k^2<6 t+k>4 t and k are positive in integers if t>k what is the value of t?

Question 1011723: t^2-k^2<6
t+k>4
t and k are positive in integers if t>k what is the value of t?

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) t^2 - k^2 < 6
2) t + k > 4
from inequality 1
(t+k)(t-k) < 6
t > k means (t-k) > 0, therefore
4 < t + k < 6 / (t - k)
4(t-k) < (t+k)(t-k) < 6
**************************************
first case
4 < t + k
4 - k < t
*************************************
second case
4(t-k) < 6
t -k < 1.5
t < k + 1.5
************************************
we have
4 - k < t < k + 1.5
4 < t+k < 2k + 1.5
2k + 1.5 > 4
2k > 2.5
k > 5/4
****************************************************
note that t and k are positive integers, therefore
k=2 and t=3
****************************************************
check answer
inequality 1
3^2 - 2^2 < 6
5 < 6
inequality 2
3 + 2 > 4
5 > 4

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