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# Algebra

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Let a and b be the solutions to 5x^2 - 11x + 4 = 0. Find 1/(a + 1) + 1/(b + 1).

Jan 21, 2022

#1
+13561
+1

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

Hello Guest!

$$5x^2 - 11x + 4 = 0\\ x^2-2.2x+0.8=0\\ x=1.1\pm \sqrt{1.21-0.8}\\ x=1.1\pm \sqrt{0.41}\\ a=1.1+ \sqrt{0.41}\\ b=1.1- \sqrt{0.41}\\$$

$$\frac{1}{a+1}+\frac{1}{b+1}=0.364921+0.685078=1.05$$

!

Jan 22, 2022
#2
+360
+1

$$5x^2-11x+4=0$$

$$x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{\left(-11\right)^2-4\cdot \:5\cdot \:4}}{2\cdot \:5}$$

$$x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{41}}{2\cdot \:5}$$

$$x_1=\frac{-\left(-11\right)+\sqrt{41}}{2\cdot \:5},\:x_2=\frac{-\left(-11\right)-\sqrt{41}}{2\cdot \:5}$$

$$x=\frac{11+\sqrt{41}}{10},\:x=\frac{11-\sqrt{41}}{10}$$

1/(a+1)=$$\frac{21-\sqrt{41}}{40}$$

1/(b+1)=$$\frac{21+\sqrt41}{40}$$

total=$$\frac{21}{20}$$

Jan 22, 2022
edited by XxmathguyxX  Jan 22, 2022
#3
+360
0

wow.. a much easier way!

Jan 22, 2022