Let a and b be the solutions to 5x^2 - 11x + 4 = 0. Find 1/(a + 1) + 1/(b + 1).
+15131 Find 1/(a + 1) + 1/(b + 1).
Hello Guest!
\(5x^2 - 11x + 4 = 0\\ x^2-2.2x+0.8=0\\ x=1.1\pm \sqrt{1.21-0.8}\\ x=1.1\pm \sqrt{0.41}\\ a=1.1+ \sqrt{0.41}\\ b=1.1- \sqrt{0.41}\\\)
\(\frac{1}{a+1}+\frac{1}{b+1}=0.364921+0.685078=1.05\)
!
+364 \(5x^2-11x+4=0\)
\(x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{\left(-11\right)^2-4\cdot \:5\cdot \:4}}{2\cdot \:5}\)
\(x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{41}}{2\cdot \:5}\)
\(x_1=\frac{-\left(-11\right)+\sqrt{41}}{2\cdot \:5},\:x_2=\frac{-\left(-11\right)-\sqrt{41}}{2\cdot \:5}\)
\(x=\frac{11+\sqrt{41}}{10},\:x=\frac{11-\sqrt{41}}{10}\)
1/(a+1)=\(\frac{21-\sqrt{41}}{40}\)
1/(b+1)=\(\frac{21+\sqrt41}{40}\)
total=\(\frac{21}{20}\)
