Question

if alpha+bita are the roots of x²+3x-2=0 then alpha+1/bita+bita+1/alpha =?​

Answer 1

Step-by-step explanation:

this is the answer of this question

Answer 2

Step-by-step explanation:

hey here is your solution

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$to \: find = \\ value \: of \: (\alpha + 1 \div \beta ) + ( \beta + 1 \div \alpha )$

$so \: here \: given \: quadratic \: equation \: is \: \\ x²+3x-2=0 \\ so \: comparing \: this \: equation \: with \: ax² + bx + c = 0 \\ we \: get \\ a = 1 \ \: \: b = 3 \: \: \: c = - 2$

$so \: we \: know \: that \\ \alpha + \beta = - b \div a \\ = - 3 \div 1 \\ = - 3 \\ moreover \: \alpha \beta = c \div a \\ = - 2 \div 1 \\ = - 2$

$so \: thus \: then \\ considering \\ \alpha + 1 \div \beta + \beta + 1 \div \alpha \\ = (\alpha + \beta) + (1 \div \alpha + 1 \div \beta ) \\ = ( \alpha + \beta ) + ( \alpha + \beta \div \alpha \beta ) \\ = - 3 + ( - 3 \div - 2) \\ = 3 + ( - 1.5) \\ = - 3 - 1.5 \\ = - 4.5$