Warm up problem 1
If you are just waking up or just got on brilliant, here is a great problem to warm up your mind with. I am beginning a new set of problems that will be titled "warm up problems". In this set, I will be posting about 1-2 mainly easy to medium level problems to warm up with. Hope you enjoy!
If the minimum value of can be expressed as a/b for positive co prime integers a,b. Find a+b.
The answer is 5947.
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1 solution
We take the derivative and are left with
2 x 3 + 2 x 2 − 8 x − 8 = 0 .
Next, we factor it to
( x + 1 ) ( x + 2 ) ( 2 x − 4 ) = 0
∴ x = − 1 , − 2 , 2
Thus plugging in the possible values of x in the above equation to the original one, we find y=5944/3 to be the minimum value @ x=2. Thus our answer is 5947