If |x|=2 and |y|=3, what is the difference between the maximum and the minimum values of x^3 + y^2? Please explain the answer. Thanks! :))

Question

ash2326 · Answer

Good question:)
@average_student Tell me what is |x|?

anonymous · Answer

it's absolute value of x

anonymous · Answer

please help, @ash2326

ash2326 · Answer

We are given
$$|x|=2 => x=\pm 2$$
and
$$|y|=3=>y=\pm 3$$
Do you agree with this?

anonymous · Answer

YES, I do agree! :))

ash2326 · Answer

Now we have the expression
$$x^3+y^2$$
notice that y's power is 2, so if y= +3 or -3, y^2 will be the same, what's the value of y^2?

anonymous · Answer

it's 9 :))

ash2326 · Answer

Great, but if we notice x, its power is 3
so if x=-2 what is x^3?
or if x=+2 what is x^3?

anonymous · Answer

it's 8 :))

anonymous · Answer

if x = -2 the answer is -8 :)))

anonymous · Answer

then the minimum value is -8 + 9 = 1???

ash2326 · Answer

Yeah:D find max ?

anonymous · Answer

the maximum value is 8 + 9 = 17?

anonymous · Answer

then 17 - 1 = 16. So, the answer is 16. am i right? :))

ash2326 · Answer

Yeah, you're right
great work , and you call yourself average. You're a good student:D:D

anonymous · Answer

Thank you very much for your help, @ash2326 .:))) very much appreciated. :))

ash2326 · Answer

You're welcome:D student:D