1) Does anyone know how to find x in 2^x = 3 + x without a CAS?
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2)
y = 0.125x^2 + 1.25x + 3
y = 11 + bx
Find b and then find the points of intersection
I got b = 3.25 and b = -0.75, but the book says only b = -0.75 is correct. Then for the POIs, only the ones you get from plugging in -0.75 are listed (if there are two answers, the book lists them both) (8, 5)
Now there's a diagram accompaniment so I know after using both b's that -0.75 is correct because 3.25 gives negative values and there are no negatives in the diagram. S
Assuming I haven't made any errors, my questions is there a way of knowing which value is correct without having to plug in and solve both? (because that question WAS separate and before the POI one) It doesn't make sense to me that you gotta put in two answers and when you do the next question, only one of them turns out to be correct
(this is from Maths Quest by the way, Ex 2L Q. 10c)
Thanks
EDIT:
Also this one:
y=x^2 + bx -14 and y = -9x + c intersect at (-1,
and (-3, 10). Find b and c
For the first pair, I got b = -5 and c = -17 and for the second b = -21 and c = -1
When you plug them back in, why does only the first set give the correct x values? (assuming, once again, I haven't made any errors)