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??

## Search found 8 matches

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

- 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 ...

- 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)

- 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.

- 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...

- 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...

- 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?

Pura pari nai. ami joto tuku parsi likhbo?

- Fri Oct 14, 2011 11:51 pm
- Forum: National Math Camp
- Topic: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১
- Replies:
**105** - Views:
**32679**

### Re: বাংলাদেশ অনলাইন ক্যাম্প - ২০১১

26-31st 1st term! 22 thk hoy na?