160 - Mathematics Questions Answers

Solve in integers the equation$x^2+y^2+xy={(\frac{x+y}{3}+1)}^3$

There are 8 distinct boxes and each box can hold any number of balls. A child having 4 identical balls randomly choose four boxes. Then another child having four balls, identical to the previous mentioned, again puts one ball in each of the arbitrary chosen four boxes. The probability that there are balls in at least 6 boxes is

Sir pls solve

Between two numbers, whose sum is 13/6, an even number of arithmetic means are inserted, the sum of these means exceed their number by unity. How many means are there?

$If \frac{9}{a}+\frac{24}{b}=1, a,b, \in {\mathrm{ℝ}}^{+}, prove that a^2+b^2\ge 9{( 4+\sqrt[3]{9})}^3.$