Let a , b , c are roots of equation x^3 + 8x | vedclass

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Question

$\frac{b c}{\left(-b^{3}\right)\left(-c^{3}\right)}+\frac{a c}{\left(-a^{3}\right)\left(-c^{3}\right)}+\frac{a b}{\left(-a^{3}\right)\left(-b^{3}\righ

Vedclass · Accepted Answer

$-16$

Vedclass · Answer

$\frac{b c}{\left(-b^{3}\right)\left(-c^{3}\right)}+\frac{a c}{\left(-a^{3}\right)\left(-c^{3}\right)}+\frac{a b}{\left(-a^{3}\right)\left(-b^{3}\right)}$

$=\frac{a^{2}+b^{2}+c^{2}}{a^{2} b^{2} c^{2}}=\frac{(a+b+c)^{2}-2 \Sigma a b}{(a b c)^{2}}$

$=\frac{0-16}{(-1)^{2}}=-16$

Let $a$ , $b$ , $c$ are roots of equation $x^3 + 8x + 1 = 0$ ,then the value of

$\frac{{bc}}{{(8b + 1)(8c + 1)}} + \frac{{ac}}{{(8a + 1)(8c + 1)}} + \frac{{ab}}{{(8a + 1)(8b + 1)}}$ is equal to

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Let $a$ , $b$ , $c$ are roots of equation $x^3 + 8x + 1 = 0$ ,then the value of $\frac{{bc}}{{(8b + 1)(8c + 1)}} + \frac{{ac}}{{(8a + 1)(8c + 1)}} + \frac{{ab}}{{(8a + 1)(8b + 1)}}$ is equal to