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# plz help

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Let u and v be the solutions to$$3x^2 + 5x + 7 = 0$$Find u/v +v/u.

i have tried answering this a few times but can't figure it out.

Sep 13, 2022

#1
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$${u \over v} + {v \over u} = {u^2 \over uv} + {v^2 \over uv} = {u^2 + v^2 \over uv}$$

$${u^2 + v^2 \over uv} = {(u + v)^2 - 2uv \over uv}$$

$$uv = {c \over a} = {7 \over 3}$$

$$u + v = -{b \over a} = -{5 \over 3}$$

$${(-{5 \over 3})^2 - 2({7 \over 3}) \over {7 \over 3}} = {{25 \over 9} - {14 \over 3} \over {7 \over 3}} = {-{17 \over 9}\over {21 \over 9}} = \color{brown}\boxed{-{17 \over 21}}$$

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Sep 13, 2022
#2
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