TheNightKing wrote:
Any other approach apart from re-writing the equation in the perfect square standard form? It is least one of favorites.
Thank you!
What is the minimum value of the expression 1/X^2 -1/2x +5/4
Lets take x <0, in this case 1/x^2 is +ve & -1/2x also becomes +ve
Now if x>0, for any value of x, expression 1/x^2 -1/2x will be +ve if 0<x<2...how lets take x=0.5 1/x^2= 1/0.25=4 while -1/2x= -1 so the entire expression is +ve
but when x>2 lets take x= 4, 1/4^2 = 1/16=0.0625 while -1/2x = -1/8=-0.125 hence expression becomes -ve
lets take x a large expression this entire (1/x^2 -1/2x) will not be smaller than -5/4
hence entire expression will always be more than 0
Now we are left with 2 options D or E
E is possible only when x is infinite and for any value less than infinite but as discussed for x>2 , the expression 1/x^2 -1/2x can be <0 which will make entire expression of 1/x^2-1/2x+5/4 slightly less than 5/4 which is only option D
Not sure the above helps
Please give kudos if you like