Question

$if \: \alpha \: and \beta \:$
Are the roots of
$4x {}^{2} + 3x + 7 = 0$


find
$\frac{1}{ \alpha {}^{3} } + \frac{1}{ \beta {}^{3} }$
​

Answer 1

Heya....

$\alpha + \beta = \frac{ - 3}{4}$

$\alpha \beta = \frac{7}{4}$

$\frac{1}{ \alpha {}^{3} } + \frac{1}{ \beta {}^{3} } = \frac{ \alpha {}^{3} + \beta {}^{3} }{ \alpha {}^{3} \beta {}^{3} }$

$\frac{( \alpha + \beta ) {}^{3} - 3 \alpha \beta ( \alpha + \beta )}{( \alpha \beta ) {}^{3} }$

$\frac{ \frac{ - 27}{64} - 3 \times \frac{7}{4} \times \frac{3}{4} }{( \frac{7}{4}) {}^{3} }$

$\frac{225}{343}$

Hope it helps

Answer 2

HIII ....

GOOD AFTERNOON:-)

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