Question

calculate !
sqrt(1+97x98x99100)
by using algebraic concept

Answer 1

is it sqrt(1+97x98x99x100)? or is the last number really 99100?

Answer 2

opppss, sorry
you are right, sqrt(1+97x98x99x100)

Answer 3

alright, hold on...

Answer 4

Let x=101
\[\sqrt{1+(x-4)(x-3)(x-2)(x-1)}\]
Rearranging,
\[=\sqrt{(x-4)(x-1)(x-3)(x-2)+1}\]
\[=\sqrt{(x^2-5x+4)(x^2-5x+6)+1}\]
\[=\sqrt{[x^2-5x+4][(x^2-5x+4)+(2)]+1}\]
\[=\sqrt{(x^2-5x+4)^2+2(x^2-5x+4)+1}\]
what's inside the radical sign is a perfect square of the form u^2 + 2u +1
\[=\sqrt{[(x^2-5x+4)+(1)]^2}\]
\[=x^2-5x+5\]
change x back to 101 and simplify. :)

Answer 5

Part II, using algebraic concept,
\[101^2=(100+1)^2=100^2+2(100)(1)+1^2=10000+200+1=10201\]

Answer 6

hahaha

Answer 7

nice trick...
but why do u let x=101, may i take x=97,98,99,or 100 ? it will work too?

Answer 8

I dunno if it will work for other numbers. I encountered a similar problem and what I used was x=101 haha

Answer 9

okokokok...^^
thanks