If m^2 - n^2 > 0 and m + n < 0 , which of the following MUST be true? ~ (Answer choices are in Description!)

Question

A) m - n > 0

B) n - m > 0

C) n - m < 0

D) m - n < 0

E) n² - m² >0

Answer 1

Hey 

first if m^2-n^2>0 then (m-n)(m+n)>0

we know that m+n<0

therefore m-n must be negative

in other words m-n<0

remember multiplying two negatives gives a positive

since we know one is already negative therefore the other one must also be negative

for m^2-n^2>0 to hold

 

Answer 2

m² - n² > 0

 

m² - n² = ( m + n)(m - n)

 

m + n < 0   It is a negative number

 

Tlherefor  D) m - n < 0  is Correct

 

Also:  B)  n -m > 0

 

becomes      0 > m - n

 

So B and D are Correct