## Question

junior college 2 | H1 Maths

Anyone can contribute an answer, even non-tutors.

##### Walking

chevron_right

Hi does anyone knows how to solve this?

Date Posted: 1 year ago
Views: 116

clear {{ downvoteCount * -1 }} Downvotes
##### Ivan Sim Wan Leong's answer
1st
Date Posted: 1 year ago
Walking
1 year ago
Can I use number line?
Ivan Sim Wan Leong
1 year ago
If use number line have to trial and error. Using calculus can find the precise turning point
Walking
1 year ago
Turning points prove real roots?
Ivan Sim Wan Leong
1 year ago
Turning points mean maximum and minimum value
Walking
1 year ago
But how to show x is real
Ivan Sim Wan Leong
1 year ago
Solutions to turning points are values of x where max and min point occur
Ivan Sim Wan Leong
1 year ago
Don't need to prove x is real. It is assumed to be real in the question.
Ivan Sim Wan Leong
1 year ago
So the qns is something like " If x is real, find max and min value of the expression"
Walking
1 year ago
Why
Walking
1 year ago
Aaaa
Walking
1 year ago
I am so confuse
Ivan Sim Wan Leong
1 year ago
Cos x is always more than min value; or less than max value. By finding the min and max and i can prove the inequality
Ivan Sim Wan Leong
1 year ago
Min and max values can be found by equating its dy/dx = 0.
Ivan Sim Wan Leong
1 year ago
The easiest way is to plot the graph of the expression. There u can see the max and min point
Jiayang
1 year ago
What you've found is the local min/max which may not be the absolute min/max. I think you need to further show that it tends to a certain value as x tends to ±∞.

And I think the qn has an error, it should include equality, ie ≤ and ≥
Mark Thong
1 year ago
I also think the question's inequility signs are wrong. And there's a non-calculus proof presented in Answer 2.
clear {{ downvoteCount * -1 }} Downvotes
Date Posted: 1 year ago
Jiayang
1 year ago
Hmmmm I think you got the qn upside down. The qn is if x is real then prove the inequality. Not given the given the inequality, prove that x is real.
Mark Thong
1 year ago
Hmm.. i think you didn't follow my reasoning and conclusion. :)
Note the double implication i used on each step, and in the end i mentioned "implying backwards".
Jiayang
1 year ago
I mean can you start off like that and do the "double implication". Issit legit?
Mark Thong
1 year ago
The question is.. Is the logic Of the proof sound And correct?

A <=> B <=> C <=> D
Hence D => A

Correct?
Jiayang
1 year ago
Yeap I get your logic but I just thought given the way the qn is asked, direct proofs make more sense ie, start with -(x-3)²≤0≤11(x+3)²
Instead of going by your way of "indirect" proof I suppose? I'm not sure actually, I'm not a math major :/
Mark Thong
1 year ago
But in the first place, how woud you know to start with -(X-3)² ≤ 0 ≤ 11(x+3)² ?
So your "direct approach" is merely working backwards.

Neither am i a math major.. ;)
Walking
1 year ago
I didn't get it...
Walking
1 year ago
Wow why can you add the equal there
Walking
1 year ago
What is the meaning of implying backwards
Walking
1 year ago
qn meaning?
Walking
1 year ago
A B C D there I didn't get it too...
Jiayang
1 year ago
Yeap work backwards. This is akin to finding the epsilon when doing limits problems. They begin with some rough work and then start the actual proof by working backwards from there. I mean your logic is fine, it's just the presentation seems awkward to me :/
Maybe we should stick to calculus hahaha