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Evaluate Prove that there are exactly three right-angled triangles whose sides are integers while the area is numerically equal to twice the perimeter. Problem 86 (^ - ) Let a convex

Evaluate Prove that there are exactly three right-angled triangles whose sides are integers while the area is numerically equal to twice the perimeter. Problem 86 (^ - ) Let a convex

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Plz solve problem 85 with explanation i will give you upvote
Problem 83 ) At a party, assume that no boy dances with every girl but each girl dances with at least one boy. prove that there are two couples gb and g0 b0 which dance whereas b doesn't dance with g0 and b0 doesn't dance with g. Problem 84 (¯ Z10Z10 -… Z 1 0 cos2 n 1 2n (x1 + x2 + ·.. + xn) o dx1 dx2 ·. dxn. Problem 85 Evaluate Prove that there are exactly three right-angled triangles whose sides are integers while the area is numerically equal to twice the perimeter. Problem 86 (* polygon P be contained in a square of side one. Show that the sum of the squares of the sides of P is less than or equal to 4. Problem 87 ) Evaluate limn→0 ) Let a convex Prove that among any ten consecutive integers at least one is relative prime to each of the others. Problem 88 Let f(x) = al sin(x) + a2 sin(2x)+ ·… + an sin(nx), where aj are real numbers. Given that |f(x)|<|sin(x)| for all real x, prove that |a1 + 2a2 + …· + nan| < 1.
Transcribed Image Text:Problem 83 ) At a party, assume that no boy dances with every girl but each girl dances with at least one boy. prove that there are two couples gb and g0 b0 which dance whereas b doesn't dance with g0 and b0 doesn't dance with g. Problem 84 (¯ Z10Z10 -… Z 1 0 cos2 n 1 2n (x1 + x2 + ·.. + xn) o dx1 dx2 ·. dxn. Problem 85 Evaluate Prove that there are exactly three right-angled triangles whose sides are integers while the area is numerically equal to twice the perimeter. Problem 86 (* polygon P be contained in a square of side one. Show that the sum of the squares of the sides of P is less than or equal to 4. Problem 87 ) Evaluate limn→0 ) Let a convex Prove that among any ten consecutive integers at least one is relative prime to each of the others. Problem 88 Let f(x) = al sin(x) + a2 sin(2x)+ ·… + an sin(nx), where aj are real numbers. Given that |f(x)|<|sin(x)| for all real x, prove that |a1 + 2a2 + …· + nan| < 1.
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