The main reason u are not getting support even after such good content is that your channel name is salogic, but if someone searches sa logic, then your channel does not appear, so plz get a better name for your channel related to maths..For example Maths GO!
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In brain. 1 m...
216-125...
Both x & y have to be positive
Very nice! ❤
x = 6, y = 5 because x³ - y³ = 6³ - 5³ = 216 - 125 = 91
Yes, you are right! ❤
X =4
Y=-3
Very Nice! ❤
X 6
Y 5
You are right! ❤
The main reason u are not getting support even after such good content is that your channel name is salogic, but if someone searches sa logic, then your channel does not appear, so plz get a better name for your channel related to maths..For example Maths GO!
Noted. very nice suggession! ❤
Soient x et y entiers, tels que x^3 - y^3 = 91.
x^3 - y^3 = 91
=> (x-y)(x² + xy + y²) = 91
On va lister tous les diviseurs de 91 :
91 n'est pas divisible par 3, 9, 5, 10, 2, 4, 6 et 8 pour les chiffres.
Testons les autres :
91
= 1 * 91
= 7 * 13
= 13 * 7
= 91 * 1
Notons que x^3 > y^3 donc x > y.
Ainsi les diviseurs entiers de 91, sont 1, 7, 13 et 91.
Soient A = x-y et B = (x² + xy + y²) :
AB = 91
Notons que x^3 > y^3 donc x > y, et donc A < B, donc A = 13 est impossible et pareillement pour A =
91.
Testons A = 1, B = 91 :
{ x-y = 1 ; x² + xy + y² = 91 }
=> { x = y + 1 ; x² + xy + y² = 91 }
=> (y+1)² + y(y+1) + y² = 91
=> y² + 2y +1 + y² + y + y² = 91
=> 3y² + 3y + 1 = 91
=> 3y² + 3y = 90
=> y² + y = 30
=> y² + y - 30 = 0
Soit dY le discriminant :
dY = 1 + 4*30 = 121
y' = (-1 - 11)/2 = -12/2 = -6
y" = (-1 + 11)/2 = 10/2 = 5
Ce qui donne :
x' = y' + 1 = -5
x" = y" + 1 = 6
Ce qui donne la solution S'={ {x:-5, y:-6}, {x:6, y:5} }.
Vérifions S'1:
x^3 - y^3
= -5^3 - -6^3
= -125 - -36*6
= -125 + 216
= 91 : OK
Vérifions S'2:
x^3 - y^3
= 6^3 - 5^3
= 216 - 125
= 91 : OK
Testons A = 7, B = 13 :
{
x-y = 7
x² + xy + y² = 13
}
=>
{
x = y + 7
x² + xy + y² = 13
}
=> (y+7)² + y(y+7) + y² = 13
=> y² + 14y + 49 + y² + 7y + y² = 13
=> 3y² + 21y + 49 = 13
=> 3y² + 21y + 36 = 0
Soit dY = 21² -36*3*4 = 441 - 36*12 = 441 - 432 = 9
y' = (-21 - 3)/6 = -24/6 = -4
y" = (-21 + 3)/6 = -18/6 = -3
Ce qui donne :
x' = y' + 7 = -4 + 7 = 3
x" = y" + 7 = -3 + 7 = 4
Ce qui donne la solution S"={ {x:3, y:-4}, {x:4, y:-3}}.
Vérifions S"1:
x^3 - y^3
= 3^3 - (-4)^3
= 27 - -64
= 27 + 64
= 91 : OK
Vérifions S"2:
x^3 - y^3
= 4^3 - (-3)^3
= 64 + 27
= 91 : OK
Ainsi nous avons 4 solutions :
{ {x:3, y:-4}, {x:4, y:-3}, {x:-5, y:-6}, {x:6, y:5} }
Very nice! ❤
x=6 and y=5
Very nice! ❤
Why did nobody mention x = -5, and y = -6? Than: x³ - y³ = (-5)³ - (-6)³ = -125 - (-216) = -125 + 216 = 91
Very nice! ❤