solve this any genius for two for 100 points
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hey mate see the attachment
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ax² + bx + c =0
alpha + beta = -b/a
a.alpha + a.beta = -b
a.alpha + b = -a.beta ------(1)
in the same way ,
a.beta + b = -a.alpha -----(2)
alpha.beta = c/a
a.alpha.beta = c ----------(3)
={alpha /( a.beta + b)}³ -{ beta /( a.beta +b)}³
put equation (1)and (2) here
={ alpha/( -a.beta)}³ -{ beta/( -a.alpha)}³
=-alpha/a³.beta³ + beta /a³alpha³
=(-alpha⁴ + beta⁴)/(a.alpha.beta)³
=(beta² -alpha²)(beta²+alpha²)/(a.alpha.beta)³
=(beta -alpha)(alpah-beta)(b²/a² -2c/a)/(c)³
beta -alpha =±√(b²/a² -4c/a)
use this ,
=(±√(b²/a² -4c/a))(-b/a)(b²/a² -2c/a)/c³
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