Find-the-positive-integer-solution-of-the-equation-x-3-y-3-911-xy-49-

Question Number 155480 by mathdanisur last updated on 01/Oct/21

Find the positive integer solution

of the equation :

x^{3} + y^{3} = 911 (xy + 49)

Answered by Rasheed.Sindhi last updated on 01/Oct/21

x^{3} + y^{3} = 911 (xy + 49)

(x + y) (x^{2} - xy + y^{2}) = 911 (xy + 49)

x + y = 911 \land x^{2} - xy + y^{2} = xy + 49

x + y = 911 \land {(x - y)}^{2} = 49

x + y = 911 \land x - y = \pm 7

2 x = 911 \pm 7

x = \frac{911 \pm 7}{2} = 459, 452

x = 459 : y = 911 - x = 911 - 459 = 452

x = 452 : y = 911 - x = 911 - 452 = 459

(x, y) = (459, 452), (452, 459)

Commented by mathdanisur last updated on 01/Oct/21

Very nice S er thank you

Commented by otchereabdullai@gmail.com last updated on 08/Oct/21

nice

Commented by Rasheed.Sindhi last updated on 08/Oct/21

T h a n k s!