Question

Сравни
1÷48+1÷50 и 2÷49
1÷11 и 2÷21+1÷23
(1÷2×2÷5)² и (1÷2)²×(2÷5)²
(1÷2÷2÷5)² и (1÷2)²÷(2÷5)²
Даю 55 баллов

Answer 1

1) (1/48+1/50)   >  2/49
НОЗ (48,49,50)=48*49*25=58800
48= 6*8= 2*2*2*2*3
49=7*7
50=5*10=2*5*5
1/48+1/50 = (1*25*49 + 1*24*49)/ 58800= (1225+1176)/58800=2401/58800
2/49 = (2*48*25)/ 58800 = 2400/58800
2401 / 58800  >  2400/5880
2) 1/11  <    2/21+1/23
НОЗ ( 11,21,23) =  11*21*23= 5313
2/21 + 1/23= 506/5313+ 231/5313= 737/5313
1/11= 483/5313
483/5313 < 737/5313
3) (1/2+2/5)² >  (1/2)² х (2/5)²
(1/2 х 2/5)² = ( 5)²= 25
(1/2)² х (2/5)² = 1/4 х 4/25 = 1/25 
25 > 1/25
4)  (1/2 : 2/5) ²  =  (1/2)²: (2/5)²
(1/2 : 2/5) ² = ( 1/2 х 5/2)² = (5/4)²= 25/16 = 1 9/16
(1/2)² : (2/5)² = 1/4 :  4/25 = 1/4 х 25/4 = 25/16= 1 9/16