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GoldRush18
Group Title
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
 2 years ago
 2 years ago
GoldRush18 Group Title
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
 2 years ago
 2 years ago

This Question is Closed

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
this is a Hard one for me
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
??? \[ x^4  \frac{y^4}{xy}\]
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
let me try to write that one better hold on
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
\[ \frac{x^4  y^4}{xy}\]
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
\[x^4y^4\div xy\] Simplify
 2 years ago

experimentX Group TitleBest 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!!!
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
well this question has 3 parts to it
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
you got this?
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
nope i dont fully understand it
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
now replace \(x\) by \(y+1\)
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
LOL ... i forgot the question!!
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
denominator is \(y+1y=1\) numerator is \[(y+1)^4y^4=(y+1+y)((y+1)^2+y^2)\]
 2 years ago

satellite73 Group TitleBest 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?
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
so replace x=y+1 into the first question?
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
thats what i see on the paper and i double checked
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
either way i think its correct nonetheless
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
\[(y+1)^4y^4=(y+1+y)((y+1)^2+y^2)\] \[=((y+1)+y)((y+1)^2+y^2)\] \[=(y+1)^3+y(y+1)^2+y^2(y+1)+y^2\]
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
is this for the third part
 2 years ago

satellite73 Group TitleBest 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 )
 2 years ago

GoldRush18 Group TitleBest 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
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
deduce that \[(y+1)^4y^4<4(y+1)^3\]
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
sorry .. i was busy somewhere!! i'll see
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
so far i have this \[(y+1)^4y^4=(y+1)^3+y(y+1)^2+y^2(y+1)+y^3\]
 2 years ago

GoldRush18 Group TitleBest 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
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
y^3<(y+1)^3 y(y+1)^2<(y+1)^3 so on ..
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
y^2(y+1) < (y+1)^3 so, \[ (y+1)^3+y(y+1)^2+y^2(y+1)+y^2 < (y+1)^3 + (y+1)^3 + (y+1)^3 + (y+1)^3 = 4(y+1)^3\]
 2 years ago

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

experimentX Group TitleBest ResponseYou've already chosen the best response.1
so, \[ (y+1)^4  y^4 < 4(y+1)^3\]
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
OK i get it now
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
thanks @satellite73 and @experimentX :)
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

experimentX Group TitleBest ResponseYou've already chosen the best response.1
you mean equation 2 ??
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

experimentX Group TitleBest 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!!
 2 years ago

satellite73 Group TitleBest 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
 2 years ago

GoldRush18 Group TitleBest ResponseYou've already chosen the best response.0
maybe there was a typo because in maths alot of errors are made
 2 years ago

experimentX Group TitleBest 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!!
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.2
got it. backwards parentheses and missing y confused the heck out of me
 2 years ago
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