CMr \(\dfrac{40^2+51^2+91^2}{79^2}=\dfrac{40^4+51^4+91^4}{79^4}\)
chứng minh rằng
a) \(1000^2+1003^2+1a5^2+1006^2=1002^2+1002^2+1004^2+1007^2\)
b) \(\dfrac{40^2+51^2+91^2}{79^2}=\dfrac{40^4+51^4+91^4}{79^4}\)
HD: a) xét
b) đặt 40=a; 51=b
Câu a : B-A= 10012 +10022 +10042 +10072 -10002-10032-10052-10062
=(10012-10002)+(10022-10032) (10042-10052)+(10072-10062)
HĐT số 3= (1001-1000)*(1001+1000)+(1002-1003)*(1002+1003)+(1004-1005)*(1004+1005)+(1007-1006)*(1007+1006)
=2001 -2005-2009+2013=0
vậy A=B
Chứng minh \(\frac{40^4+51^4+91^4}{79^4}=\frac{40^2+51^2+91^2}{79^2}\)
Chứng minh \(\frac{40^2+51^2+91^2}{79^2}=\frac{40^4+51^4+91^4}{79^4}\)
\(\frac{40^2+51^2+91^2}{79^2}\)= \(\frac{2\times\left(40^2+51^2+91^2\right)}{2\times79^2}\)
=> dpcm
Chứng minh: \(\frac{40^4+51^4+91^4}{79^4}=\frac{40^2+51^2+91^2}{79^2}\)
Vế thứ nhất lớn hơn hoặc bằng chứ.Thay a,b,c vào rồi cm bất đẳng thức là xong
Chứng minh rằng: \(\frac{40^2+51^2+91^2}{79^2}=\frac{40^4+51^4+91^4}{79^4}\)
Chứng minh: \(\frac{40^2+51^2+91^2}{79^2}\)= \(\frac{40^4+51^4+91^4}{79^4}\)
Tính tổng
\(\dfrac{51}{53}+\dfrac{55}{57}+\dfrac{61}{63}+\dfrac{69}{71}+\dfrac{79}{81}+\dfrac{91}{93}\)
\(\dfrac{51}{53}+\dfrac{55}{57}+\dfrac{61}{63}+\dfrac{69}{71}+\dfrac{79}{81}+\dfrac{91}{93}\)
\(=\left(\dfrac{52}{53}-\dfrac{1}{53}\right)+\left(\dfrac{56}{57}-\dfrac{1}{57}\right)+\left(\dfrac{62}{63}-\dfrac{1}{63}\right)+\left(\dfrac{70}{71}-\dfrac{1}{71}\right)+\left(\dfrac{80}{81}-\dfrac{1}{81}\right)+\left(\dfrac{92}{93}-\dfrac{1}{93}\right)\)
\(=\left(1-\dfrac{1}{53}-\dfrac{1}{53}\right)+\left(1-\dfrac{1}{57}-\dfrac{1}{57}\right)+\left(1-\dfrac{1}{63}-\dfrac{1}{63}\right)+\left(1-\dfrac{1}{71}-\dfrac{1}{71}\right)+\left(1-\dfrac{1}{81}-\dfrac{1}{81}\right)+\left(1-\dfrac{1}{93}-\dfrac{1}{93}\right)\)
\(=\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)+\left(1-0\right)\)
\(=1+1+1+1+1+1\)
\(=6\)
1.Tính
79 x 11 + 2800 + 40 26475 x 36 - 76945 : 5
2.Điền dấu < > =
7/2.........4/79 27/9..........2 51/17...........3/1
3.Điền số thích hợp
...../32 = 21/24 6/15 = 18/........ ...../13 = 121/143
4.Điền số thích hợp vào chỗ chấm
a, 50 kg 5hg =................ g 12500 g =.............kg .............hg
500kg=..............tạ 450 tạ=....................tấn
b,2 giờ 78 phút=...............phút 10 thế kỉ=.................năm
1500 năm=..............thế kỉ 2 năm=.................tháng
c,8 dam 5m=..............m 5m 7cm=.....................mm
d,78500 dm vuông=............m vuông 7m vuông 5cm vuông=............cm vuông
5cm vuông 7mm vuông =..........mm vuông 3km vuông 9m vuông=.......m vuông
3:
28/32=21/24
6/15=18/45
11/13=121/143
2:
7/2>4/79
27/9>2
51/17=3/1
Tính hợp lí
a)\(\dfrac{2-\dfrac{1}{3}+\dfrac{1}{4}}{2+\dfrac{1}{6}-\dfrac{1}{4}}+\dfrac{\dfrac{3}{5}-\dfrac{1}{4}+\dfrac{5}{10}}{\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{2}{5}}\)
b)\(\dfrac{\dfrac{5}{79}+\dfrac{5}{83}+\dfrac{1}{17}}{\dfrac{17}{79}+\dfrac{17}{83}+\dfrac{1}{5}}\)
a,=\(\dfrac{\left(2-\dfrac{1}{3}+\dfrac{1}{4}\right).12}{\left(2+\dfrac{1}{6}-\dfrac{1}{4}\right).12}\)+\(\dfrac{\left(\dfrac{3}{5}-\dfrac{1}{4}+\dfrac{1}{2}\right).20}{\left(\dfrac{1}{2}+\dfrac{3}{4}-\dfrac{2}{5}\right).20}\)
=\(\dfrac{24-4+3}{24+2-3}\) +\(\dfrac{12-5+10}{10+15-8}\)(nhân từng số hạng với 12;20)
=\(\dfrac{23}{23}\)+\(\dfrac{17}{17}\) =1+1=2
b,=\(\dfrac{5.\left(\dfrac{1}{79}\right)+5.\left(\dfrac{1}{83}\right)+\dfrac{1}{17}}{17.\left(\dfrac{1}{79}\right)+17.\left(\dfrac{1}{83}\right)+\dfrac{1}{5}}\)=\(\dfrac{5.\left(\dfrac{1}{79}+\dfrac{1}{83}\right)+\dfrac{1}{17}}{17.\left(\dfrac{1}{79}+\dfrac{1}{83}\right)+\dfrac{1}{5}}\)