Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
let x and y be positive real numbers such that x does not equal to y.
i. simplify x^4y^4/ xy
ii. hence, or otherwise, show that
(y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3.
iii. Deduce that (y+1)^4y^4 < 4(y+1)^3
 one year ago
 one year ago
let x and y be positive real numbers such that x does not equal to y. i. simplify x^4y^4/ xy ii. hence, or otherwise, show that (y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3. iii. Deduce that (y+1)^4y^4 < 4(y+1)^3
 one year ago
 one year ago

This Question is Closed

GoldRush18Best ResponseYou've already chosen the best response.0
this is a Hard one for me
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
??? \[ x^4  \frac{y^4}{xy}\]
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
let me try to write that one better hold on
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\[ \frac{x^4  y^4}{xy}\]
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
\[x^4y^4\div xy\] Simplify
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
(x^2)^2  (y^2)^2 = (x^2  y^2)(x^2 + y^2) I think you can do the rest!!!
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
well this question has 3 parts to it
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
nope i dont fully understand it
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
\[\frac{x^4  y^4}{xy}=\frac{(x+y)(xy)(x^2+y^2)}{xy}=(x+y)(x^2+y^2)\] is the first part
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
now replace \(x\) by \(y+1\)
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
LOL ... i forgot the question!!
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
denominator is \(y+1y=1\) numerator is \[(y+1)^4y^4=(y+1+y)((y+1)^2+y^2)\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
it is not clear to me what you wrote for the second part, but now algebra should give us what want. what was the second part supposed to be?
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
you wrote \[(y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3.\] but the parentheses are messed up
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
so replace x=y+1 into the first question?
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
thats what i see on the paper and i double checked
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
either way i think its correct nonetheless
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
\[(y+1)^4y^4=(y+1+y)((y+1)^2+y^2)\] \[=((y+1)+y)((y+1)^2+y^2)\] \[=(y+1)^3+y(y+1)^2+y^2(y+1)+y^2\]
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
is this for the third part
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
i do not get what you want for the second part. there is a hanging plus sign and an extraneous )
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
i got the second part alright its the third part i don't get let me rewrite it here
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
@experimentX do you know what the second part is supposed to be? it makes no sense to me. there is a typo of some sort
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
deduce that \[(y+1)^4y^4<4(y+1)^3\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
sorry .. i was busy somewhere!! i'll see
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
so far i have this \[(y+1)^4y^4=(y+1)^3+y(y+1)^2+y^2(y+1)+y^3\]
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
the second one to me is just simply saying the answer u got in first one just replace x=y+1 thats all
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
yes, but it has a specific form it wants you to put it in, and i don't know what that form is supposed to be
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
y^3<(y+1)^3 y(y+1)^2<(y+1)^3 so on ..
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
y^2(y+1) < (y+1)^3 so, \[ (y+1)^3+y(y+1)^2+y^2(y+1)+y^2 < (y+1)^3 + (y+1)^3 + (y+1)^3 + (y+1)^3 = 4(y+1)^3\]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
looks like equation went off screen \[(y+1)^3+y(y+1)^2+y^2(y+1)+y^2 < 4(y+1)^3 \]
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
so, \[ (y+1)^4  y^4 < 4(y+1)^3\]
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
thanks @satellite73 and @experimentX :)
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
maybe it is supposed to be this: \[(y+1)^4y^4=(y+1)^3+y(y+1)^2+y^2(y+1)+y^3\] well i don't
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
@experimentX do you have any idea what the right side is supposed to be in equation 2? i mean i get the inequality, just not what the expression is supposed to be
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
this line \[(y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3\] has no meaning to me
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
you mean equation 2 ??
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
i got this \[(y+1)^4y^4=(y+1)^3+y(y+1)^2+y^2(y+1)+y^3\] , but it is not clear to me what we are supposed to turn it in to
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
i think there a typho there!! a^n  b^n = (a  n) (a^(n1) + a^(n2)b + a^(n3)b^2 + ... +b^(n1)) this is the pattern!!
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
ok i got that. i won't worry about it i know there is a typo but i am not sure what it was supposed to be instead
 one year ago

GoldRush18Best ResponseYou've already chosen the best response.0
maybe there was a typo because in maths alot of errors are made
 one year ago

experimentXBest ResponseYou've already chosen the best response.1
\( (y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3. \) ^ \( (y+1)^4y^4=(y+1)^3+(y+1)^2+(y+1)y^2+y^3. \) ^ also, \( (y+1)^4y^4=(y+1)^3+(y+1)^2+(y+1)y^2+y^3. \) ^ < y missing here .... i think ti should be what you got!!
 one year ago

satellite73Best ResponseYou've already chosen the best response.2
got it. backwards parentheses and missing y confused the heck out of me
 one year ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.