CPhill

December, for me....

BTW.....I wonder which month all the ugly people were born in ????

(4-5i)(-8+i)(1-2i)    taking this in parts, we have

(4-5i) (-8 + i)   =    -32 + 40i +4i - 5i² = -32 + 44i + 5   =  -27 + 44i

(-27 + 44i) ( 1 - 2i)  =  -27 + 44i + 54i - 88i²  = 61 + 98i

What's the question here???

HAHAHAHAHAHAHAHAHAHAHAHAHAHA  !!!!!!!!!!!!!!!!!

(Ain't  I crafty ????????)

Yeah...I thought it was a mistake......it was still pretty crafty the way you figured that out!!...I can see it NOW........this was my usual experience in Physics class.....I always understood it better AFTER the tests!! (LOL!!!)

Notice one thing more about this one , if we want to use Melody's algebraic method....taking it from here

5(x-2)(x-4)² < 3(x-2)²(x-4)

We can do this to simplify things.....

5(x-2)(x-4)² - 3(x-2)²(x-4) < 0      factoring, we have

(x-2)(x-4)[5(x-4) - 3(x-2)] < 0

(x-2)(x-4)[5x- 20 -3x +6 ] < 0

(x-2)(x-2)[2x -14] < 0

2(x-2)(x-4)(x-7) < 0

(x-2)(x-4)(x-7) < 0

And notice that we don't have to use the Factor Theorem at all....the "roots" (i.e., critical interval values) are right in front of us !!!

Be careful here.....mutiplying by "a" isn't the same thing a dividing by "a"....

For instance, if we have

3x = 6    

Then I would want to divide both sides by 3 to solve for x.   But, if I multiplied both sides by 3, I would have

9x = 18

And I would only have a multiple of the first equation  ....   and wouldn't be any closer to solving it than I was originally.....!!!

Alan....where did  the "56°" come from???

Did you mean "53°"  instead ???

Great answer from Anonymous !!

Here's another possibility:

5 + 5 + 5 ≠ 550     (and that makes the equation "correct" ....well, at least in a "perverse" way!!!)

l x - 42.04 l = 23.24

Just solve both of these equations:

x - 42.04 = 23.24          and        x - 42.04 = -23.24

You will have two different answers for "x"