Search found 8 matches

by Rashik ctg
Wed Oct 26, 2011 3:44 pm
Forum: National Math Camp
Topic: Exercise 1.7 (iii) [Section 1, BOMC-2011]
Replies: 20
Views: 6262

Re: Exercise 1.7 (iii) [Section 1, BOMC-2011]

Prove which cases??? ****noted ones??

a≤b≤1
=> b-a≤1
=> (b-a)/1-ab ≤1 [1≥b≥a so ab≤1 1-ab ≥0]

does that satisfy??
by Rashik ctg
Wed Oct 26, 2011 2:07 pm
Forum: National Math Camp
Topic: Exercise 1.7 (iii) [Section 1, BOMC-2011]
Replies: 20
Views: 6262

Re: Exercise 1.7 (iii) [Section 1, BOMC-2011]

1.7(i) 0 ≤ a ≤ b ≤ 1. Does that imply, a ≤ 1, b ≥ 0???? if so , we can't divide (b - a) by (1 - ab) . if (ab = 1), (1- ab = 0) ?? b ≥ a => b - a ≥ 0 => (b - a) / 1 - ab ≥ 0 [ a≤b≤1 , ab≤1, 1 - ab not equal to 0] **** again, so, b≤1 => b - a ≤ 1 [ a≤b≤1 ]**** => (b - a)/ 1 - ab ≤ 1 [1-ab>0] so 0 ≤(b ...
by Rashik ctg
Tue Oct 25, 2011 10:27 pm
Forum: National Math Camp
Topic: Triangle Inequality: (Bangladesh Online Math Camp)
Replies: 34
Views: 10447

Re: Triangle Inequality: (Bangladesh Online Math Camp)

If y < 0 , is this ok? U can multiply with y iff y>0. (Mayb)
by Rashik ctg
Tue Oct 25, 2011 10:09 pm
Forum: National Math Camp
Topic: Triangle Inequality: (Bangladesh Online Math Camp)
Replies: 34
Views: 10447

Re: Triangle Inequality: (Bangladesh Online Math Camp)

x^2 + y^2 + 2xy grter or equal 2 zero. That is the prob.
by Rashik ctg
Tue Oct 25, 2011 9:46 pm
Forum: National Math Camp
Topic: Triangle Inequality: (Bangladesh Online Math Camp)
Replies: 34
Views: 10447

Re: Triangle Inequality: (Bangladesh Online Math Camp)

1st case x,y is ≥ o x^2+xy+y^2≥ 0 no doubt. 2nd case x,y ≤ 0 , then x^2 + y^2 ≥ 0 and xy ≥ 0 so , x^2+xy+y^2≥ 0 3rd case now, x ≥ 0 , y ≤ 0 or y≥ 0, x ≤ 0 x^2 + y^2 ≥ 0 but can't prove the rest. x^2+ y^2 - 2xy ≥ 0 x^2+ y^2 ≥ 2xy i need to prove, x^2+ y^2 ≥ xy if x ≥ 0 , y ≤ 0 or y≥ 0 , x ≤ 0 2xy ≤ x...
by Rashik ctg
Tue Oct 25, 2011 9:43 pm
Forum: National Math Camp
Topic: Triangle Inequality: (Bangladesh Online Math Camp)
Replies: 34
Views: 10447

Re: Triangle Inequality: (Bangladesh Online Math Camp)

1st case x,y is ≥ o x^2+xy+y^2≥ 0 no doubt. 2nd case x,y ≤ 0 , then x^2 + y^2 ≥ 0 and xy ≥ 0 so , x^2+xy+y^2≥ 0 3rd case now, x ≥ 0 , y ≤ 0 or y≥ 0, x ≤ 0 x^2 + y^2 ≥ 0 but can't prove the rest. x^2+ y^2 - 2xy ≥ 0 x^2+ y^2 ≥ 2xy i need to prove, x^2+ y^2 ≥ xy if x ≥ 0 , y ≤ 0 or y≥ 0 , x ≤ 0 2xy ≤ x...
by Rashik ctg
Tue Oct 25, 2011 8:58 pm
Forum: National Math Camp
Topic: Triangle Inequality: (Bangladesh Online Math Camp)
Replies: 34
Views: 10447

Re: Triangle Inequality: (Bangladesh Online Math Camp)

$x^2 + xy + y^2 \geq 0$
Pura pari nai. ami joto tuku parsi likhbo?