Questions and answers by

mathsen

Questions (11)

Let ABC be a triangle such that angle ACB = 135 degrees. Prove thatAB^2 = AC^2 + BC^2 + ¡Ì2 x AC x BC.
1. 2 answers
2. 672 views
Let P and Q be the points on the sides AB and BC of a triangle ABC respectively such that BP = 3PA and QC = 2BQ. Let K be the
1. 1 answer
2. 1,300 views
In a quadrilateral ABCD, the diagonal AC bisects angle BAD and AB = BC = CD. Prove that the other diagonal, BD, bisects angle
1. 1 answer
2. 1,876 views
In a pentagon ABCDE, AB = AE, BC = ED and BD = EC. Prove that AC = AD.
1. 1 answer
2. 681 views
Prove that if real numbers a, b and c satisfya + b + c > 0, ab + ac + bc > 0 and abc > 0, then each of a, b and c is positive.
1. 0 answers
2. 583 views
Prove thata^4 + b^4 + c^4 ¡Ý b^2ac + c^2ab holds for all real numbers a, b and c.
1. 0 answers
2. 431 views
Simplify:2/1! - 3/2! + 4/3! - 5/4! + ... + 2010/2009! - 2011/2010!, where k! denotes the product of all integers from 1 up to k,
1. 0 answers
2. 459 views
Is it possible to arrange the integers from 1 to 240 in a table with 15 rows and 16 columns so that the sum of the numbers in
1. 0 answers
2. 471 views
For which real values of b do the equationsx^3 + b x^2 + 2bx - 1 = 0 and x^2 + (b-1)x + b = o have a common root?
1. 1 answer
2. 485 views
Prove that if p, q, r and s are odd integers, then the equationx^10 + p x^9 - q x^7 + r x^4 - s = 0 has no integer roots.
1. 0 answers
2. 471 views
Prove that:20^22 - 17^22 + 4^33 - 1 is divisible by 174.
1. 0 answers
2. 402 views