Question

If b³+a²c+ac² = 3abc , then the relation between the roots of the equation ax²+bx+c=o is?

Answer 1

Answer:

Step-by-step explanation:

> b³ + a²c + ac² = 3abc  

-->\frac{b^3 + a^2c + ac^2}{c^2} = \frac{3abc}{c^2} \\ = [\frac{b}{c} ]^3 + [ \frac{a}{c} ]^2 + \frac{a}{c} = 3 \frac{a}{c} \frac{b}{c} \\ =-[ \alpha + \beta ]^3 + [\frac{1}{ \alpha \beta} ]^2 + \frac{1}{ \alpha \beta} = 3[ \alpha + \beta ][ \alpha \beta ] \\ 
= - \frac{ \alpha^5+ 3 \alpha^4 \beta ^3 +3 \alpha ^3 \beta ^4+ \alpha ^2 \beta ^5- \alpha  \beta -1}{ \alpha ^2 \beta ^2} = 3 \alpha  \beta [ \alpha + \beta]

Well friend... This is an irreducible form where only two Integer soln. exist..

--> a = -1 ; b = 1  ;;; or ;;; a = 1; b = -1

hope u will understand

Answer 2

$a = {b}^{2}$