# The Equation \$X^3 + Y^3 = Z^3\$ Has No Integer Solutions

If displaystylex+y+z=6 & displaystylex^2+y^2+z^2=14 & displaystylex^3+y^3+z^3=36 then what are displaystylex,y,z ?
displaystyleleftlbracex,y,z ight brace=leftlbrace1,2,3 ight brace Explanation: displaystyle1+2+3=6displaystyle1^2+2^2+3^2=1+4+9=14 ...

Bạn đang xem: The equation \$x^3 + y^3 = z^3\$ has no integer solutions

The answer depends on what sorts of numbers you are looking for. Assuming you're looking for positive integers, at least one of the three numbers (let's say z) has khổng lồ be at least 5, since 4^3 + 4^3 + 4^3 = 192
Take your second equation và solve for Y in terms of X. Then, plug this into your first equation, & into the 3rd equation to get two equations that have X and Z as variables. Then in the first ...
(Spoiler: This answer contains the word “SEX”.) It depends. If you want three real numbers x,y,z satisfying x^3+y^3+z^3=33 then there are infinitely many, & they are very easy lớn find. If ...

Xem thêm: Tả Lớp Học Bằng Tiếng Anh Viết Về Lớp Học (4 Mẫu), Viết Về Lớp Học Của Em Bằng Tiếng Anh

With some forethought, you can bring it down to one case to kiểm tra directly, which turns out to lớn be a solution. A previous version of this answer examined the equation thủ thuật 7, which led to lớn 16 cases ...

Xem thêm: Trung Tâm Bảo Hành Máy Giặt Electrolux Mỹ Đình Uy Tín 0936, Sửa Máy Giặt Electrolux Tại Mỹ Đình 0986687668

https://math.stackexchange.com/questions/1762614/what-is-the-way-to-solve-the-following-system-of-equations
Assuming the last equation is meant khổng lồ be x^3 + y^3 + z^3 = 64, we can consider squaring (x + y + z): 16 = (x+y+z)^2 = (x^2 + y^2 + z^2) + 2(xy + yz + xz) = 24 + 2(xy + yz + xz) và so (xy + yz + xz) = -4 ...
More Items     left< eginarray l l 2 & 3 \ 5 và 4 endarray ight> left< eginarray l l l 2 và 0 & 3 \ -1 & 1 và 5 endarray ight>      EnglishDeutschEspañolFrançaisItalianoPortuguêsРусский简体中文繁體中文Bahasa MelayuBahasa Indonesiaالعربية日本語TürkçePolskiעבריתČeštinaNederlandsMagyar Nyelv한국어SlovenčinaไทยελληνικάRomânăTiếng Việtहिन्दीঅসমীয়াবাংলাગુજરાતીಕನ್ನಡकोंकणीമലയാളംमराठीଓଡ଼ିଆਪੰਜਾਬੀதமிழ்తెలుగు