Question

if alpha and beta are the roots of the equation ax²-bx+b=0 then prove that √alpha/beta + √beta/alpha-√b/a=0​

Answer 1

Answer:

roots are α and β

\begin{gathered}\alpha + \beta = - \frac{b}{a} = - \frac{ - b}{a} \\ \alpha \beta = \frac{c}{a} = \frac{b}{a} \\ \sqrt{ \frac{ \alpha }{ \beta } } + \sqrt{ \frac{ \beta }{ \alpha } } \\ \frac{ \sqrt{ \alpha } }{ \sqrt{ \beta } } + \frac{ \sqrt{ \beta } }{ \sqrt{ \alpha } } \\ \frac{ \alpha + \beta }{ \sqrt{ \alpha \beta } } \\ \frac{ \frac{ - b}{a} }{ \sqrt{ \frac{b}{a} } } \\ - \frac{b \sqrt{a} }{a \sqrt{b} } \\ - \sqrt{ \frac{b}{a} }\end{gathered}

α+β=−

a

b

=−

a

−b

αβ=

a

c

=

a

b

β

α

+

α

β

β

α

+

α

β

αβ

α+β

a

b

a

−b

−

a

b

b

a

−

a

b