Question

a/b whole cube + b/c whole cube+c/a whole cube -3​

Answer 1

Hii...here is your ans...

a cube + b cube + c cube + 3a(ab+ac+bc)+3b(ab+bc+ac)+3c(ac+bc+ab)-3abc

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Answer 2

$\Big(\frac{a}{b}\Big)^{3} + \Big(\frac{b}{c}\Big)^{3} + \Big(\frac{c}{a}\Big)^{3}$

$= [\frac{a}{b}+ \frac{b}{c} + \frac{c}{a}][ \Big(\frac{a}{b}\Big)^{2} + \Big(\frac{b}{c}\Big)^{2} + \Big(\frac{c}{a}\Big)^{2} - \frac{a}{b} \times \frac{b}{c} - \frac{b}{c} \times \frac{c}{a} - \frac{c}{a} \times \frac{a}{b} ] + 3\times \frac{a}{b} \times \frac{b}{c}\times \frac{c}{a}]$

$\pink { x^{3}+y^{3}+z^{3} } \\\pink {= (x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)+3xyz}$

$= [\frac{a}{b}+ \frac{b}{c} + \frac{c}{a}][\frac{a^{2}}{b^{2}}+ \frac{b^{2}}{c^{2}}+ \frac{c^{2}}{a^{2}} - \frac{a}{c} - \frac{b}{a} - \frac{c}{b} ] + 3$

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