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imqwerty
 one year ago
short fun question :D
imqwerty
 one year ago
short fun question :D

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imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3\[[x^2]+[2x]=3x\]where [ . ] >greatest integer function Find the values of x which satisfy this equation \[x \in [0,6]\]

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.32.666 is wrong :) please tell ur method too (:

baru
 one year ago
Best ResponseYou've already chosen the best response.3ehh.......its the probably the most bone headed way to approach it lol :)

baru
 one year ago
Best ResponseYou've already chosen the best response.3RHS has to lie between 0 and 18. so i can substitute integer values for LHS which give me less than 18. so thats 0,1,2,3. if the RHS has to be an integer then, x=0,0.333,0.666.....3. sooo.. ya...i actually tried all of them

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3(: ok here is my approach the greatest integer function will always give out an integer :D so [x^2] >an integer [2x]>an integer [x^2]+[2x]>integer+integer =integer :D so 3x has to be an integer so x has to be integer so x can be either 0,1,2,3,4,5,6 so because x is an integer we can write \[[x^2]+[2x]=x^2+2x\] so now we are left with a quadratic \[x^2+2x=3x \]solving it we get x=1,0 :)

baru
 one year ago
Best ResponseYou've already chosen the best response.3but x need not be an integer, i.e 0.3333*3=1 (ish)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3we take exact values B)

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3do u agree that the LHS will give an integer?

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3and LHS=RHS so RHS will also be an integer?

baru
 one year ago
Best ResponseYou've already chosen the best response.3not necessarily,...if that was the case then mentioning greatest integer function would have been pointless.

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3greatest integer function was just to confuse (:

baru
 one year ago
Best ResponseYou've already chosen the best response.3@imqwerty aagh...i think 2.666 would work. greatest integer function rounds down so [2.66]=2 therefore LHS=8 and 3*2.666=8 (almost). i guess the answer to this is matter of opinion aswell XD

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3XD but it can never be an integer haha :D it is almost close tho ahaha

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\(x=5/3\) is also a solution http://www.wolframalpha.com/input/?i=solve+floor%28x%5E2%29%2Bfloor%282x%29%3D3x%2C+0%3C%3Dx%3C%3D6

baru
 one year ago
Best ResponseYou've already chosen the best response.35/3 =1.666 [5/3]=1 so LHS=3 RHS=5

mathmate
 one year ago
Best ResponseYou've already chosen the best response.1x=2.6666=8/3, but would not work. [x^2]+[2x] =[(8/3)^2]+[2*8/3] =[64/9]+[16/3] =7+5 =12 3x=3(8/3)=8 \(\ne12\) So x=8/3 does not work. But 5/3 works!

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3hmmm..so while doing such questions we must also search for rational solutions with the denominator which gets cancelled ... :)
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