Properties of number

Question

Hi I need help with this question. specifically part (b) and (d)

x and y are two integers such that−5(x^2+y) is a positive number. Determine whether each of the following expression is positive, negative, 0, or “No unique answer”.

a)y - negative
b)x+y - negative
c)−y - positive
d)x−y - positive
e)(x^2+y)/y - positive
f)x^2 - no unique answer
g)x^2+y^2 - positive

Thank you

sivatx2 · Answer

𝒙 and 𝒚 are two integers such that−5(𝒙^2+𝒚) is a positive number. Determine whether each of the following expression is positive, negative, 0, or “No unique answer”.

a)𝒚 - negative
b)𝒙+𝒚 - negative
c)−𝒚 - positive
 d)𝒙−𝒚 - positive (INCORRECT: Must be No unique answer)
x could be negative. Note, square of a negative number is always positive.Also, it could be a very very large number, "negatively". and could make x-y a negative value. Since both positive and negative values are possible, the choice would be "No unique answer". 
e)(𝒙^2+𝒚)/𝒚 - positive
  f)𝒙^2 - no unique answer (INCORRECT: Must be positive)
Irrespective of whether x is positive or negative integer, x^2 is always a positive integer. 
 
g)𝒙^2+𝒚^2 - positive

Durgaa · Answer

Hi

The answers I have written are correct. I need an explanation as to why parts b and d have such answers.

ash124 · Answer

From
𝒙 and 𝒚 are two  integers  such that−5(𝒙^2+𝒚) is a  positive number

from this equation:
−5(𝒙^2+𝒚)
 
 𝒙^2 is always +tive and to negative sign given outside of brackets 
𝒙^2+𝒚 < 0 
you can take some numbers as well
 
y = -10(y will always be a -tive integer as 𝒙^2 is always +tive and we need a negative (𝒙^2+𝒚) ) 
x can be positive or negative but 𝒙^2 should be less than |y|
x = 2 or -2
𝒙^2 = 4

b)𝒙+𝒚 - negative
 as 𝒙^2 should be less than |y|

-2-10 = -12
2-10 = -8
always -tive

d)𝒙−𝒚 - positive

in same way
-2+10 = 8
2+10 = 12 
always +tive

Durgaa · Answer

Hi ash124

i understand now. thank you.

ash124 · Answer

Good to know

Thanks for asking

Properties of number

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