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Sat 11 Feb, 2006 10:33 am
Hey Ppl,
I got some very tricky problems to be solved...i need to submit it on friday to my prof..but i already have 2 tests this week..so i am not able to find time to solve this proofs...if any one can solve them..it wud be gr8.
here we go..
Prove/Disprove the following proposition
1. x is real, (x sqr)>(x)
2. x is real, (xsqr)>(x+1)
3.n is natural no, (n cube-n) is divisible by 3.
4. x is real , (x cube) > (x sqr)
5.x,y, real, x sqr+ y sqr=9.
6.n is natural no, (n cube +2n) is divisible by 3.
7. N is natural, 2(n+2) (less or equal to)(n+2) sqr.
do reply if u know the proof..
1. False---find a real number where X^2<X
2. False---find a real number where X^2<X+1
3. True---proof by induction show its true for some natural number (usually 0 or 1, but you can pick one at random) assume it it true for any natural n then show it is true for n+1
4. False--find a real number where X^3<X^2
5. False---find real x,y s.t x^2+y^2<>9
6. True--proof by induction show its true for some natural number, assume it's true for n then show it would be true for some n+1
7. True--proof by contradiction Assume it isn't true and then find that solutions are not natural numbers.
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