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Mymensingh Higher Secondary 2018#7

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Mymensingh Higher Secondary 2018#7

Posted: Mon Mar 12, 2018 8:08 pm
by samiul_samin
What is the lowest value of $(x^2-8x)(x^2-8x+10)$?

Re: Mymensingh Higher Secondary 2018#7

Posted: Mon Mar 12, 2018 8:21 pm
by samiul_samin
Answer
$\fbox {-25}$
Solution
Let,$x^2-8x=a$,
So,Let,$f(a)=a(a+10)=a^2+10a$
$\Rightarrow f '(a)=2a+10$
$\Rightarrow f ' '(a)=2$
So,we will get the lowest value if $2a+10=0\Rightarrow 2a=-10\Rightarrow a=-5$
If we plug the value of $a$ in the given expression,we will get our answer $\fbox {-25}$
I think ,there is more easy and low tech solution available.So,please post more easy solution(without using calculas).

Re: Mymensingh Higher Secondary 2018#7

Posted: Sun Feb 17, 2019 9:22 am
by samiul_samin
samiul_samin wrote: ↑
Mon Mar 12, 2018 8:08 pm
 What is the lowest value of $(x^2-8x)(x^2-8x+10)$?
This is actually question no 6.
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