Giúp với, mai thi rồi!
Cho : \(a+b\inℤ\); \(a^2+b^2\inℤ\)và \(a^4+b^4\inℤ\). Chứng minh rằng: \(a^3+b^3\inℤ\)
Monh thầy cô và các CTV giúp đỡ ạ! Em cảm ơn trước!
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Khách
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Những câu hỏi liên quan
12 tháng 12 2021
\(A=1+2+2^2+...+2^{119}\\ =\left(1+2\right)+\left(2^2+2^3\right)+...+\left(2^{118}+2^{119}\right)\\ =\left(1+2\right)+2^2\left(1+2\right)+...+2^{118}\left(1+2\right)\\ =\left(1+2\right)\left(1+2^2+...+2^{118}\right)\\ =3\left(1+2^2+...+2^{118}\right)⋮3\\ \\ A=1+2+2^2+...+2^{119}\\ A=\left(1+2+2^2\right)+...+\left(2^{117}+2^{118}+2^{119}\right)\\ A=\left(1+2+2^2\right)+...+2^{117}\left(1+2+2^2\right)\\ =\left(1+2+2^2\right)\left(1+...+2^{117}\right)\\ =7.\left(1+...+2^{117}\right)⋮7\)
Còn các ý sau bạn tự làm theo cách này tiếp nha!
VN
Võ Ngọc Phương
CTVHS
VIP
28 tháng 12 2023
Ta có: ( Giải chi tiết )
Giả sử có \(-a\) và \(b\) thì:
\(\left(-a\right).b\) ( Vì " - " nhân " + " bằng " - " \(\Rightarrow\left(-\right)< 0\)) \(\Rightarrow\) Loại A.
\(\left(-a\right).b\) ( Như trên ) \(\Rightarrow\) Giữ B.
\(\left(-a\right)+b\).
TH1: (-a) + b = -c ⇒ -c < 0. vd: (-3) + 2 = -1 < 0
TH2: (-a) + b = c ⇒ c > 0. vd: (-1) + 2 = 1 > 0
\(\Rightarrow\) Loại C.
\(\left(-a\right).b\) ( Như trường hợp a,b ) \(\Rightarrow\) Loại D.
Vậy chọn phương án B.
NN
0
B
15 tháng 4 2021
uses crt;
var e,f,i,a,b,c,d: byte;
begin
clrscr;
write('Tu so = '); readln(e);
write('Mau so = '); readln(f);
a:=e;
b:=f;
writeln('Phan so ban dau: ',e,'/',f);
while E <> F do
if E > F then E:=E-F
else F:=F-E;
If e <> 1 then
begin
a:=a div e;
b:=b div e;
write('Phan so toi gian: ',a,'/',b);
end
else write('Phan so da toi gian, ',a,'/',b);
readln
end.
NV
1
24 tháng 12 2020
Bring a large saucepan filled with water to a boil.Add the bean sprouts to the saucepan and blanch for 3 to 5 seconds.Place a handful of noodles (fresh or cooked dried noodles) in a longhandle noodle strainer and blanch for 5 to 10 seconds. ...Place the warmed noodles in the bowl.Cho mik tick nhé!
NV
2
5 tháng 1 2021
Pho is one of my favorite foods. Pho is the most popular and special dish in our country, Vietnam. There are two main kinds of Pho: Pho with beef and Pho with chicken. Pho is served in a bowl with a specific cut of white rice noodles in clear beef broth, with slim cuts of beef (steak, fatty flank, lean flank, brisket). Chicken Pho is made using the same spices as beef, but the broth is made using only chicken bones and meat, as well as some internal organs of the chicken, such as the heart, the undeveloped eggs and the gizzard. I always enjoy a bowl of hot and spicy Pho for breakfast. Mornings are a special time for pho in Vietnam. I love Pho and I can eat it every morning without boring.
ND
1
AL
14 tháng 5 2021
There are many types of natural disasters, storms are one of them, a storm is a turbulent state in the atmosphere and a type of extreme weather.There are many types of storms: Snowstorms: a very heavy snow phenomenon. thick with strong winds. Usually occurs in cold or temperate countries. Sand tornado: also known as sand demon, is a phenomenon of sand swept up very high, occurring at noon in desert areas. To: is the phenomenon of wind speeding up suddenly, accompanied by strong thunderstorms. Thunderstorms: are storms accompanied by thunder, heavy rain or hail. Tornado: is a phenomenon of a circular swirling air stream extending from a thunderstorm cloud down to the ground, especially in that a thunderstorm can descend on empty fields (rural areas) and cities. Fire storm: is a way to call intense fires that have created their own convection system and wind, making it extremely large and difficult to control or extinguish. Tropical cyclones are rapidly rotating storm systems characterized by a center of low pressure, strong winds and a spiral cloud structure that produces heavy rain. lots of homes. The bigger the storm, the more loss of life and property. Storms often break trees and damage homes. A hurricane with a tornado can sweep people and houses away, break trees, cause crop damage, and cause accidents to planes and boats. Therefore, we must take timely measures to prevent storms, we must resist our house carefully, so we can prevent a little harm from storm.
Chứng minh:
\(a^3+b^3=\left(a+b\right)^3-3ab\left(a+b\right)\)
Ta có: \(a+b\in Z\)
và \(a^2+b^2=\left(a+b\right)^2-2ab\in Z\Rightarrow2ab\in Z\)
\(a^4+b^4=\left(a^2+b^2\right)^2-2a^2b^2\in Z\Rightarrow2a^2b^2\in Z\)
Đặt 2ab=k , k thuộc Z => \(4a^2b^2=k^2\Rightarrow2a^2b^2=\frac{k^2}{2}\in Z\Rightarrow\frac{k}{2}\in Z\)=> ab thuộc Z
=> \(a^3+b^3\in Z\)
Em chưa hiểu chỗ này: \(\frac{k^2}{2}\inℤ\Rightarrow\frac{k}{2}\inℤ\)