An algebra problem by Razing Thunder

Algebra Level 4

The value of ( 201 4 2 2020 ) × ( 201 4 2 + 4025 ) × ( 2015 ) ( 2010 + 1 ) × ( 2010 + 3 ) × ( 2010 + 6 ) × ( 2010 + 7 ) \frac{(2014^{2} - 2020) \times (2014^{2} + 4025) \times (2015)}{(2010+1) \times (2010+3) \times (2010 + 6) \times (2010+7)} = ?


The answer is 2015.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

\(Let x=2014.\\
Exp.=\dfrac{(x^2-2020)*(x^2+4025)*2015}{2011*2013*2016*2017}\\ ~~~~~~\\ ~~\\
(x^2-2020)*(x^2+4025)=\{x^2~-~(x+6)\}*\{x^2~+~(2x-3)\}\\~~~\\
=x^4~+~(x-9)x^2~-~(2x^2+3x-18)\\ ~~\\
{\color{red}{=x^4~+~x^3~-~11x^2~-~9x+18.}}\\~~~\\ ~~\\
2011*2013*2016*2017=(x-3)*(x-1)*(x+2)*(x+3)\\ ~~~\\


=x^4~+~(-3-1+2+3)x^3~+~\{(3-6-9)~+~(-2-3)~+~6\}x^2~+~(-6-18+9+6)x~+~18\\ ~~~\\
{\color{red}{=x^4~+~x^3~-~11x^2~-~9x~+~18.}}\\~~~\\~~~\\
Exp.= \dfrac 1 1*2015=\color {blue}{\Large 2015} . \)

Since I used calculator to know the answer, I used the above solution.

Razing Thunder
Jul 10, 2020

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...