A mineral extraction team recovers a a\,a tonnes of ore in the first week. Each subsequent week, the amount extracted increases by a constant d d\,d tonnes.
The total tonnage extracted over the first 8 weeks is equal to the square of the total tonnage extracted over the first 2 weeks.
Show that 2a+7d=a2+ad+14d22a + 7d = a^2 + ad + \frac{1}{4}d^22a+7d=a2+ad+41d2
Given that the amount of ore extracted in week 5 is exactly 10 tonnes, find the smallest possible value of aaa.
