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victoria1 victoria1
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7 years ago
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.

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habibahabiba
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7 years ago
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victoria1 Author
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7 years ago Edited: 7 years ago, mjvictor13
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

Post Merge: 7 years ago

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.)
wrote...
2 years ago
Thank you
wrote...
Educator
A year ago
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.)


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