Solving the Impossible: Squaring a Negative Number

[thomas49th]

For (a) I got x = $$\sqrt{-11}$$ which you can't do as you can't square root a negitive number, I can't help but feel I am wrong

 

[cristo]

For (a) I got x = $$\sqrt{-11}$$ which you can't do as you can't square root a negitive number, I can't help but feel I am wrong

Well, for that reason I would say that Bill is wrong; not you!

 

[thomas49th]

and for (b) I began be substituting y =2x - 2 into the y²

x² + (2x-2)(2x-2) = 25

5x² -8x -21 = 0

am I doing the right thing so far. When I used the quadratic formula I got a decimal number, not a whole number and the question doesn't say anything about rounding to a degree of accuracy so I presume the answer is whole numbers

 

[arildno]

No, you may presume that the answer is to be given exactly in b)!

That is you have the two solutions:
$$x=\frac{-(-8)\pm\sqrt{(-8)^{2}-4*5*(-21)}}{2*5}=\frac{8\pm\sqrt{484}}{10}=\frac{8\pm{22}}{10}$$
As it happens, you get rational solutions here, otherwise, the exact solutions would involve square root symbols explicitly.

 

[cristo]

and for (b) I began be substituting y =2x - 2 into the y²

x² + (2x-2)(2x-2) = 25

5x² -8x -21 = 0

am I doing the right thing so far. When I used the quadratic formula I got a decimal number, not a whole number and the question doesn't say anything about rounding to a degree of accuracy so I presume the answer is whole numbers

What do you get when you solve this quadratic equation? The answer does not necessarily have to be a whole number, especially if it is only a short decimal. The solution to this equation is such that it can easily be written exactly.

 

[HallsofIvy]

Or, to put it another way,
5x²- 8x+ 21= (5x+ 7)(x- 3)= 0

 

[thomas49th]

i must of made an error in typing it into my calculator. For one of x's solutions I got somthing like 4.926537173 (i pressed random keys after the 3.s.f). Ill check over my work now...

 

[thomas49th]

okay, when typing it in I think I calculated the stuff inside the root wrong

anyway the answer:

x = -7 or 3
y = -16 or 4

 

[arildno]

Eeeh??
Whatever are you talking about?

 

[thomas49th]

never mind, but I've posted the (i think correct answers now above).

However I am concerned that -16² + -7² don't equal 25

 

[HallsofIvy]

arildno suggested
$$x=\frac{-(-8)\pm\sqrt{(-8)^{2}-4*5*(-21)}}{2*5}=\frac{8\pm\sqrt{484}}{10}=\frac{8\pm{22 }}{10}$$

and I told you that 5x²- 8x+ 21= (5x+ 7)(x- 3)= 0.

How could you possibly get "x = -7 or 3" from that?

 

[thomas49th]

(8 + 22)/10 = 3
(8-22)/10 = 1.4

woops

EDIT: Making y 4 or 4.8

 

[HallsofIvy]

Well, I would have said 7/5 but but I grew up BC (before calculators).

 

[arildno]

Actually, I would say -7/5..

 

[thomas49th]

$$x=\frac{-(-8)\pm\sqrt{(-8)^{2}-4*5*(-21)}}{2*5}=\frac{8\pm\sqrt{484}}{10}=\frac{8\pm{22 }}{10}$$

8+22 = 30/10 = 3
8-22 = -14/10 = -1.4

feed that into the equation y = 2(x) - 2

2(3) - 2 = 6- 2 = 4
2(-1.4) - 2 = -2.8-2 = -4.8

I would think that must be right?

 

[HallsofIvy]

Yes, that is correct. Now be sure to pair them correctly: the solutions to the pair of equations is x= 3, y= 4 and x= -1.4, y= -4.8.