Try this beautiful problem from Algebra based on Least Possible Value.
What is the least possible value of \(((x+1)(x+2)(x+3)(x+4)+2019)\)
where (x) is a real number?
But try the problem first...
AMC-10A (2019) Problem 19
Pre College Mathematics
To find out the least positive value of \((x+1)(x+2)(x+3)(x+4)+2019\), at first we have to expand the expression .\(((x+1)(x+2)(x+3)(x+4)+2019)\) \(\Rightarrow (x+1)(x+4)(x+2)(x+3)+2019=(x^2+5x+4)(x^2+5x+6)+2019)\)
Let us take \(((x^2+5x+5=m))\)
then the above expression becomes \(((m-1)(m+1)+2019)\) \(\Rightarrow m^2-1+2019\) \(\Rightarrow m^2+2018\)
Can you now finish the problem ..........
Clearly in \((m^2+2018).......(m^2)\) is positive ( squares of any number is non-negative) and least value is 0
can you finish the problem........
Therefore minimum value of \(m^2+2108\) is \(2018\) since \(m^2 \geq 0\) for all m belongs to real .
From the video below, let's learn from Dr. Ashani Dasgupta (a Ph.D. in Mathematics from the University of Milwaukee-Wisconsin and Founder-Faculty of Cheenta) how you can shape your career in Mathematics and pursue it after 12th in India and Abroad. These are some of the key questions that we are discussing here: