inequalities help (1 Viewer)

[tommykins]

let x = (v-3)/2

(v-3)/2(v-1)/2(v+1)/2(v+3)/2 >= -1
(v+3)(v-3)(v+1)(v-1) >= -16
v⁴ - 10v² + 9 >= -16
v⁴ - 10v² + 25 >= 0
(v² - 5)² >= 0
:. true

I don't think you can do that, as you've assumed the original statement is true.

Teacher + peers have told me you need to find something that's already true, then manipulate it toawrds the statement.

 

[lolokay]

how about..

(v² - 5)² >= 0
v⁴ - 10v² + 25 >= 0
v⁴ - 10v² + 9 >= -16
(v+3)(v-3)(v+1)(v-1) >= -16
(v-3)/2(v-1)/2(v+1)/2(v+3)/2 >= -1
let x = (v-3)/2
x(x+1)(x+2)(x+3) >= -1

???

 

[tommykins]

回复: Re: inequalities help

That's fine

You never cease to amaze me.

 

[lyounamu]

let x = (v-3)/2

(v-3)/2(v-1)/2(v+1)/2(v+3)/2 >= -1
(v+3)(v-3)(v+1)(v-1) >= -16
v⁴ - 10v² + 9 >= -16
v⁴ - 10v² + 25 >= 0
(v² - 5)² >= 0
:. true

lolokay, tell me: how did you come about establishing that x = (v-3)/2?

 

[lolokay]

lolokay, tell me: how did you come about establishing that x = (v-3)/2?

I wanted to make the expression into the multiple of two differences of 2 squares (so it would become a quadratic that I could complete the square with), so to do this you would make x = v - 3/2, but it's a bit less messy if you just let x = (v-3)/2 so you can get rid of the fractions

 

[Affinity]

He is claiming:

1.) statement * holds for all v.
2.) * must hold in the particular case when v is substituted by 2x+3

 

[adosh]

HEY could some one please help me for inequalities 4 unit.. all i need to know is that,,,,if the question asks us to prove that this inequality is true. eg x+1/x>2 well for any inequality question,,, are we allowed to start wiht the inequality adn then manipulate it in such a way so taht we get an answer taht we know is correct ,,and then can we conclude that the initial question inequality is correct ,,,,or must we start the question form somewhere else and through manipulation indirectly arrive at the question and hence conclude that it is correct.......thanks alot

 

[doink]

divide both sides by x.

for x > 0 LHS is +ve and RHS is -ve hence true

for x < 0 do what first post on this page did.

 

[tommykins]

HEY could some one please help me for inequalities 4 unit.. all i need to know is that,,,,if the question asks us to prove that this inequality is true. eg x+1/x>2 well for any inequality question,,, are we allowed to start wiht the inequality adn then manipulate it in such a way so taht we get an answer taht we know is correct ,,and then can we conclude that the initial question inequality is correct ,,,,or must we start the question form somewhere else and through manipulation indirectly arrive at the question and hence conclude that it is correct.......thanks alot

You must do that.

 

[midifile]

HEY could some one please help me for inequalities 4 unit.. all i need to know is that,,,,if the question asks us to prove that this inequality is true. eg x+1/x>2 well for any inequality question,,, are we allowed to start wiht the inequality adn then manipulate it in such a way so taht we get an answer taht we know is correct ,,and then can we conclude that the initial question inequality is correct ,,,,or must we start the question form somewhere else and through manipulation indirectly arrive at the question and hence conclude that it is correct.......thanks alot

I agree with tommy.

But what you can do is on the blank pages on the back of the lined paper, start from the inequality you are trying to prove and manipulate into something that is true. Then once youve got it, cross that out, and write it backwards on the lined papers, starting from the true statement