Question

If a, b and c are the roots of the equation x^3 - 3x^2 + 2x + 1 = 0, then what is the value of =
1/a + 1/b + 1/c​

Answer 1

Step-by-step explanation:

$\huge\blue{\underline{\underline{\bf Question:-}}}$

$If \: \: a \: b \: c \: \: are \: roots \: \: of \: \: \\ {x}^{3} - 3 {x}^{2} + 2x + 1 \\ \\ find \: \: the \: \: value \: \: of \implies \\ \\ \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$

$\huge\blue{\underline{\underline{\bf Answer:-}}}$

$Lets \: \: simplify \: \: the \: \: value... \\ \\ \implies \frac{1}{a} + \frac{1}{b} + \frac{1}{c} \\ \\ \implies \frac{a + b}{ab} + \frac{1}{c} \\ \\ \implies \boxed{\frac{ac + bc + ab}{abc} }$

$\\ \\ Now, \: \: from \: \: given \: \: equation... \\ \\ {x}^{3} - 3{x}^{2} + 2x + 1 = 0 \\ \\ comparing \: \: with \: \: general \: \: equation.. \\ \\ \large \boxed{a {x}^{3} + b {x}^{2} + cx + d = 0 } \\ \\ a + b + c = \frac{ - b}{a} = \frac{3}{1 } = 3 \\ \\ ab + bc + ca = \frac{c}{a} = \frac{2}{1} = 2 \\ \\ a \times b \times c = \frac{d}{a} = 1 \\ \\ so \: \: value \: \: of \: \: \frac{ab + bc +ca }{a \times b \times c} \: \: is \: \: directly.. \\ \\ \implies \frac{2}{1} \\ \\ \huge \boxed{ \implies \frac{ab + bc + c}{a \times b \times c} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 2 }$