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Title: Solve Diophantus’s Problem B–8: To find two numbers such that their difference a Post by: victoria1 on Apr 24, 2016 Solve Diophantus’s Problem B–8: To find two numbers such that their difference and the difference of their cubes are equal to two given numbers. (Write the equations as x−y=a, x3−y3=b. Diophantus takes a=10, b= 2120.) Derive necessary conditions on a and b that ensure a rational solution.
Title: Re: Solve Diophantus’s Problem B–8: To find two numbers such that their difference a Post by: habiba on Apr 24, 2016 Content hidden
Title: Re: Solve Diophantus’s Problem B–8: To find two numbers such that their difference a Post by: victoria1 on Apr 28, 2016 can you solve this problem.
Brahmagupta asserts that if AB C D is a quadrilateral in- scribed in a circle, as in Exercise 7, then if s = 1 (a + 2 b + c + d), the area of the quadrilateral is given by S = √(s − a)(s − b)(s − c)(s − d) (Fig. 8.12). Prove this re- sult as follow 14. Show that the diameter D of the largest circle that can be in- scribed in a right triangle with legs a and b and hypotenuse c is given by D = 2ab/(a + b + c). (This is a generaliza- tion of problem 16 of chapter 9 of the Nine Chapters, which uses the specific 8-15-17 triangle.) Title: Re: Solve Diophantus’s Problem B–8: To find two numbers such that their difference a Post by: Marisa Rojo on Oct 17, 2021 Thank you
Title: Re: Solve Diophantus’s Problem B–8: To find two numbers such that their difference a Post by: bio_man on Apr 27, 2022 Show that the diameter D of the largest circle that can be in- scribed in a right triangle with legs a and b and hypotenuse c is given by D = 2ab/(a + b + c). (This is a generaliza- tion of problem 16 of chapter 9 of the Nine Chapters, which uses the specific 8-15-17 triangle.) (https://biology-forums.com/gallery/45/6_27_04_22_11_20_07.png) (https://biology-forums.com/index.php?action=gallery;sa=view&id=45018) |