Arithmetic

The integers r and s are distinct, r not=0 and s not= 0. If r^2 s^2= -rs, which of the following must be ture

is it r^2 - s^2 = -rs ?? Please post the complete prob.

This is all what it's written in the book..

The Integer r and s are distinct, r NOT =0 and s NOT =0. If r^2 s^2= -rs, which of the following must be true?

i. r= -1
ii. s= 1
iii. r-s= 0

A) None
B) i only
C) ii only
D) iii only
E) i, ii, and iii

Page 240 Kaplan 800 Chapter 13 Question 13...
OA is A

Got u!

r^s^2 = -rs

r^2s^2+rs = 0

Take rs common factor

rs(rs+1) = 0

rs cannot be equal to 0 since its given r <> 0 and s<>0

Therefore rs+1=0
rs = -1

Either r can be -1 and s = 1 or s=-1 and r=1

I) r=-1

Need not be true

II) s=1

Need not be true

III) R-S=0

If r=-1 then s=1 or if s=-1 r=1 therefoore r-s will never be 0

None

A)


P.S

Its a must be true(always) question hence None. If it was a could be true question it would be I and II

Nice approach.. Thanks