suma kwadratów trzech kolejnych liczb nieparzystych wynosi 515 jakie to liczby?
ma wyjść 11,13,15
k - liczba całkowita dodatnia
+ + = 515
+ 4k + 1 + + 12k + 9 + + 20k + 25 = 515
+ 36k + 35 = 515
+ 36k = 480
+ 36k - 480 = 0 \\12
+ 3k - 40 = 0
Delta:
DELTA = - 4ac
DELTA = + - 4 x 1 x -40 = 9 + 160 = 169
= 13
k1 = -3 - 13 / 2 = -8
k2 = -3 + 13 /2 = 5
wybieramy 5, bo jest dodatnie
+ + =515
odp. Liczby to 11, 13, 15
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k - liczba całkowita dodatnia
+ + = 515
+ 4k + 1 + + 12k + 9 + + 20k + 25 = 515
+ 36k + 35 = 515
+ 36k = 480
+ 36k - 480 = 0 \\12
+ 3k - 40 = 0
Delta:
DELTA = - 4ac
DELTA = + - 4 x 1 x -40 = 9 + 160 = 169
= 13
k1 = -3 - 13 / 2 = -8
k2 = -3 + 13 /2 = 5
wybieramy 5, bo jest dodatnie
+ + =515
+ + = 515
+ + = 515
odp. Liczby to 11, 13, 15