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# Algebra

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Find 1/(a - 1) + 1/(b - 1), where a and b are the roots of the quadratic equation 2x^2 - 9x + 2 = 0.

Jan 5, 2022

#1
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Find 1/(a - 1) + 1/(b - 1).

Hello Guest!

$$2x^2 - 9x + 2 = 0\\ x\in \{a,b\}\\ x\in \{(\frac{9}{4}+\frac{\sqrt{65}}{4} ),(\frac{9}{4}-\frac{\sqrt{65}}{4})\}$$

$$\color{blue}\frac{1}{a-1}+\frac{1}{b-1}\\ =\dfrac{1}{\frac{9}{4}+\frac{\sqrt{65}}{4}-1}+\dfrac{1}{\frac{9}{4}-\frac{\sqrt{65}}{4}-1}\\ \color{blue} =-1$$

!

Jan 5, 2022