can some one explain.. (1 Viewer)

[duy.le]

there was this question in an exam paper, could some one explain it for me. (thanks in advance)

Q. Explain the fallacy in the following argument:

-1= sqrt(-1) . sqrt(-1) = sqrt ((-1)(-1)) = sqrt (1) = 1. Hence 1 = -1

2 marks. oh and it is 4 unit

 

[Yamiyo]

I think the fallacy is that
sqrt(a) x sqrt(b) = sqrt(ab) applies iff a,b are positive.

 

[duy.le]

yeah, maybe but i think that there MAYBE another fault because the question is worth 2 but hey i might be wrong on that. thanks for the idea. sorry i dont have the answer so yeah.

 

[tommykins]

It doesn't apply because they aren't real numbers.

 

[undalay]

yeah, maybe but i think that there MAYBE another fault because the question is worth 2 but hey i might be wrong on that. thanks for the idea. sorry i dont have the answer so yeah.

Root laws do not apply for negatives
Thats the fault.

 

[duy.le]

they so thanks for the help guys, appreciate it.

 

[eliseliselise]

umm dont quote me on this... im only young!

the argument only consists of numbers that are real, not complex sooooO....!

-1= (a+ib)^2
-1= a^2 - b^2 + 2abi

therefore! a^2 - b^2=-1 abd 2ab= 0 [equating R + imag parts]

b=0 => a^2=-1 which just cant happen coz a is real!!

so. a=0 and -b^2=-1 => b= +/- 1

hence the roots are -i and i

i^2=-1 and (-i)^2 = (-1)^2 i^2=-1

sooo...

sqrt(-1) x sqrt(-1) = sqrt(1x-1) x sqrt(1x-1)=1ix1i which cannot equal sqrt{(-1)x(-1)}

so.. thats the story of the fallacy. [i think. sorry if im wrong & make u fail ur hsc. correct me if im wrong!!]

 

[Trebla]

The paper that question came from and the solutions:
http://boredofstudies.org/mirror/4u/maths_ext2_fortst03trial.pdf

 

[tommykins]

回复: Re: can some one explain..

umm dont quote me on this... im only young!

the argument only consists of numbers that are real, not complex sooooO....!

-1= (a+ib)^2
-1= a^2 - b^2 + 2abi

therefore! a^2 - b^2=-1 abd 2ab= 0 [equating R + imag parts]

b=0 => a^2=-1 which just cant happen coz a is real!!

so. a=0 and -b^2=-1 => b= +/- 1

hence the roots are -i and i

i^2=-1 and (-i)^2 = (-1)^2 i^2=-1

sooo...

sqrt(-1) x sqrt(-1) = sqrt(1x-1) x sqrt(1x-1)=1ix1i which cannot equal sqrt{(-1)x(-1)}

so.. thats the story of the fallacy. [i think. sorry if im wrong & make u fail ur hsc. correct me if im wrong!!]

Solid working and valiant attempt, your answer is correct.
Be more confident in your working, you're doing accelerated 4unit, you'll be ripping us next year ;p