Algebra proofs - Algebra equation

May 29th, 2015
Studypool Tutor
Price: $10 USD

Tutor description

Many algebra proofs are done using proof by mathematical induction. To demonstrate the power of mathematical induction, we shall prove an algebraic equation and a geometric formula with induction.

Word Count: 624
Showing Page: 1/3
Algebra Proofs:InequalitiesERHS Math Club1. Squares are positive x20, Factoring, Quadraticsa. Prove the Arithmetic Mean- Geometric Mean inequality for two variables: for all a,b0.b. Prove by multiplying by 2 and factoring as squares.c. Prove that by factoring. Conclude the AM-GM inequality for 3 variables.d. Find all values of k such that x2+y2kxy for all real numbers x and y.e. Find the largest value of k such that x4+4x2y2+y4k(x3y+xy3) for all real numbers x and y.f. Prove that x4+24x2y2+16y48x3y+32xy3 for all real x,y.g. Prove that if a>b>c>d and a+d=b+c then bc >ad. (Hint: let s=a+b. Factor bc-ad)h. Prove Aczels Inequality: if then by considering the determinant of the quadratic i. [Romanian Olympiad 1983] Let a1,a5 and x,y be real numbers such that . Prove that j. [IMO 2008/2] Prove that if , and are three real numbers, all different from ,

Review from student

Studypool Student
" Awesome! Exactly what I wanted. "
Ask your homework questions. Receive quality answers!

Type your question here (or upload an image)

1827 tutors are online

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors