China | Math Olympiad | A Very Nice Algebra Problem
HTML-код
- Опубликовано: 8 сен 2024
- GET MY EBOOKS
•••••••••••••••••••••••
Differentiation : payhip.com/b/W...
Indefinite Integration : payhip.com/b/8...
Definite Integration + Area under the Curve : payhip.com/b/1...
Trigonometry : payhip.com/b/8...
OTHER CHAPTERS : COMING SOON.....
--------------------------------------------------------------------------------
Join the channel to become a member
/ @mathbooster
x² + y² = 13
x³ + y³ = 19
find E = x + y
(x + y)² = 13 + 2xy
xy = [(x + y)² - 13]/2
(x + y)³ = 19 + 3xy(x + y)
(x + y)³ = 19 + (3/2)[(x + y)² - 13](x + y)
(x + y)³ = 19 + (3/2)(x + y)³ - 39/2(x + y)
(1/2)(x + y)³ - 39/2(x + y) + 19 = 0
E³ - 39E + 38 = 0
E³ - E - 38(E - 1) = 0
E(E + 1)(E - 1) - 38(E - 1) = 0
(E - 1)(E² + E - 38) = 0
*E = 1*
E² + E - 38 = 0
*E = (-1 ± √153)/2*
asnwer=11 isit
asnwer=1+152/2 isit