Question

If p = a(b – c), q = b(c – a), r = c(a – b) then(p/a)^3+(q/b)^3+(r/c)^3 is equal to

Answer 1

Step-by-step explanation:

3bc (c-b)+3ca (a-c)+3ab (b-a)

Answer 2

$Given \: p=a(b-c) , \:q=b(c-a) \:and \: r=c(a-b)$

$\red{ Value \: of \: \Big(\frac{p}{a}\Big)^{3} + \Big(\frac{q}{b}\Big)^{3} + \Big(\frac{r}{c}\Big)^{3}}$

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

$= (b-c)^{3} + (c-a)^{3} + (a-b)^{3}$

$= 3(b-c)(c-a)(a-b)$

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$We \:know \:that ,$

$\pink{ If \: x + y + z = 0 \:then }$

$\pink{ x^{3} + y^{3} + z^{3} = 3xyz }$

$\blue{Here , b - c + c - a + a - b = 0}$

_________________

Therefore.,

$\red{ Value \: of \: \Big(\frac{p}{a}\Big)^{3} + \Big(\frac{q}{b}\Big)^{3} + \Big(\frac{r}{c}\Big)^{3}}$

$\green { = 3(b-c)(c-a)(a-b) }$

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