proof algebra

[weak dagger]

proof that (x+y)(1/x + 1/y) >= 4

[ashen notch]

I bet you mistyped "=" in "1/x = 1/y", what operator is it supposed to be?

[weak dagger]

yeah my bad bro

its +

apologies

[ashen notch]

(x+y)((1/x)+(1/y))
= x(1/x)+x(1/y)+y(1/x)+y(1/y)
= 1+(x/y)+(y/x)+1
= 2+(x/y)+(y/x)
but x and y can be anything?

or x>0 and y>0 ?

[weak dagger]

i dont understand this at all

ik they can be anything

whats up with my prof man

[ashen notch]

if x and y can be anything then it's not always true
if x=-1 and y=1, then:
2+(-1/1)+(1/-1) = 2-1-1 = 0 (<4)

[weak dagger]

bro its supposed to be >4 not <4

[crisp kelp]

...which is exactly the problem...