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GoldRush18
 3 years 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
GoldRush18
 3 years 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

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

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

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

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

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

experimentX
 3 years ago
Best 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!!!

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

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0nope i dont fully understand it

satellite73
 3 years ago
Best 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

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

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1LOL ... i forgot the question!!

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2it 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?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2you wrote \[(y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3.\] but the parentheses are messed up

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

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

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

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

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0is this for the third part

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2i do not get what you want for the second part. there is a hanging plus sign and an extraneous )

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0i got the second part alright its the third part i don't get let me rewrite it here

satellite73
 3 years ago
Best 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

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

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

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

GoldRush18
 3 years ago
Best ResponseYou've already chosen the best response.0the second one to me is just simply saying the answer u got in first one just replace x=y+1 thats all

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2yes, 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

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

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

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

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

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2maybe 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

satellite73
 3 years ago
Best 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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2this line \[(y+1)^4y^4=(y+1)^3+(y+1)^2+)y+1)y^2+y^3\] has no meaning to me

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

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2i 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

experimentX
 3 years ago
Best ResponseYou've already chosen the best response.1i 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!!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.2ok 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

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

experimentX
 3 years ago
Best 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!!

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