## BdMO National Secondary/Higher Secondary 2018/1

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### BdMO National Secondary/Higher Secondary 2018/1

Solve:

$x^2(2-x)^2=1+2(1-x)^2$

Where $x$ is real number.

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Higher Secondary 2018/1

Solution

SYED ASHFAQ TASIN
Posts: 29
Joined: Thu Jun 02, 2016 6:14 pm

### Re: BdMO National Higher Secondary 2018/1

How do you know that x$=1$ is a solution?Trial & error?What if it had some big numbers,or fraction?
EARLY TO BED AND EARLY TO RISE,MAKES A MAN HEALTHY,WELTHY AND WISE.[\color]

SINAN EXPERT
Posts: 38
Joined: Sat Jan 19, 2019 3:35 pm
Contact:

### Re: BdMO National Secondary/Higher Secondary 2018/1

Here is the easier way to solve the problem.
শর্তমতে,
$x^{2}\left( 2-x\right) ^{2}=1+2\left( 1-x\right) ^{2}$
বা, $x^{2}\left( x-2\right) ^{2}=1+2\left( x-1\right) ^{2}$
বা, $\left\{ x\left( x-2\right) \right\} ^{2}=1+2\left( x-1\right) ^{2}$
বা, $\left\{ (x-1+1)\left( x-1-1\right) \right\} ^{2}=1+2\left( x-1\right) ^{2}$
বা, $\left\{ \left( x-1\right) ^{2}-1^{2}\right\} ^{2}=1+2\left( x-1\right) ^{2}$
বা, $\left( x-1\right) ^{4}-2\left( x-1\right) ^{2}+1=1+2\left( x-1\right) ^{2}$
বা, $y^{2}-4y=0$ $[y=x-1$ $ধরে]$

Now you can easily solve the equation.

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Higher Secondary 2018/1

SYED ASHFAQ TASIN wrote:
Wed Dec 26, 2018 9:43 pm
How do you know that x$=1$ is a solution?Trial & error?What if it had some big numbers,or fraction?
I used trial and error to get $x=1$.