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t^2 - (t-9)^2 = 9
t^2 - t^2 + 18t - 81 = 9
18t=90
[b][u]t=5[/u][/b]
Smashing, thanks. Where does the 18t come from?
Don't worry, I've got it, wasn't squaring the brackets properly. Hannah says thanks!
(A+B)^2=A^2+B^2+2AB
Ok last bit, why is it +18t not -18t ?
The first minus cancels the one within the brackets?
When you multiply out the brackets you get
t^2 - (t^2 - 18t + 81) = 9
So negate everything in the brackets
t^2 - t^2 + 18t - 81 = 9
Ok, got it now. Cheers
(A-B)^2=(A-B)(A-B)=a^2-ab-ba+b^2=a^2+b^2-2ab
A few more steps shown in the working out might help....
t^2 - (t - 9)^2 = 9
t^2 - (t - 9)(t - 9) = 9
t^2 - (t^2 - 18t + 81) = 9
t^2 - t^2 + 18t - 81 = 9
18t - 81 = 9
18t = 90
t = 5
A common mistake would be to not take the step in line 4.
That was my second mistake (forgetting 2AB being my first).
Many thanks, we're onto English now!