45 - Algebra 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?

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

The expression ax2 + 2bx + b has same sign as that of b for every real x, then the roots of equation bx2 + (b – c) x + b – c – a = 0 are (A) real and equal (B) real and unequal (C) imaginary (D) None of these

If a,b and c are positive real numbers, show that

$\frac{a}{b+c}+\frac{b}{c+a}+\frac{c}{a+b}\ge \frac{3}{2}$