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# help

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Let $$a,b,c$$ and $$d$$ be the roots of $$x^4 + 8x^3 + 9x^2 + 5x + 4 = 0.$$ Find the value of $$\frac{1}{ab} + \frac{1}{ac} + \frac{1}{ad} + \frac{1}{bc} + \frac{1}{bd} + \frac{1}{cd}.$$

Apr 16, 2019

#1
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Try making the expression you're trying to find into one big fraction. Then use Vieta's Formulas and plug coefficients in.

Apr 17, 2019
#2
+7711
+2

Let P be the value of the required expression.

$$P = \dfrac{cd+bd+bc+ad+ac+ab}{abcd} = \dfrac{\dfrac{9}{1}}{\dfrac{4}{1}} = \dfrac{9}{4}$$

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Apr 18, 2019