# 43 - Algebra Questions Answers

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

**Asked By: RATHER NOT SAY**

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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

**Asked By: KANDUKURI ASHISH**

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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?

**Asked By: PREM**

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**Joshi sir comment**

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

**Asked By: JAMES GHOSH**

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**Asked By: PREM**

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

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

**Asked By: MROY**

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**Asked By: LUFFY**

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**Joshi sir comment**

$Probabilitytogetfollowingdifferences\phantom{\rule{0ex}{0ex}}differenceprobability\phantom{\rule{0ex}{0ex}}06/36\phantom{\rule{0ex}{0ex}}110/36\phantom{\rule{0ex}{0ex}}28/36\phantom{\rule{0ex}{0ex}}36/36\phantom{\rule{0ex}{0ex}}44/36\phantom{\rule{0ex}{0ex}}52/36\phantom{\rule{0ex}{0ex}}Sorequiredprobability=1-2\left[\frac{6}{36}\left(\frac{4}{36}+\frac{2}{36}\right)+\frac{10}{36}\left(\frac{2}{36}\right)\right]\phantom{\rule{0ex}{0ex}}nowsolve\phantom{\rule{0ex}{0ex}}problemisbasedonintegralvaluessoareaisnotveryuseful$

Find Sum to n terms

x/1-x² + x²/1-x⁴ + x⁴/1-x⁸ + ....

**Asked By: LUFFY**

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**Joshi sir comment**

$\frac{x}{1-{x}^{2}}=\frac{1}{1-x}-\frac{1}{1-{x}^{2}}\phantom{\rule{0ex}{0ex}}breakalltermssimilarlyandsolve\phantom{\rule{0ex}{0ex}}$

No. of integral roots of the eqn. x^{8} - 24 x^{7} - 18x^{5} + 39 x^{2} + 1155 = 0 .

**Asked By: VAIBHAV GUPTA**

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**Joshi sir comment**

two times sign change so 2 positive roots