Answered

Westonci.ca is your go-to source for answers, with a community ready to provide accurate and timely information. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.

The reciprocal of an integer plus the reciprocal of two times the integer plus two equals 2/3   Find the integer.

Sagot :

kate200468
[tex] \frac{1}{x} + \frac{1}{2x+2}= \frac{2}{3}\ /\cdot 3x(2x+2) \ \ \ \wedge\ \ \ x \neq 0\ \ \wedge\ \ 2x+2 \neq 0\\ \\.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ x\in R-\{0;-1\}\\ \\ \frac{1}{x}\cdot 3x(2x+2) + \frac{1}{2x+2}\cdot 3x(2x+2)= \frac{2}{3}\cdot 3x(2x+2)\\ \\3(2x+2)+3x=2x(2x+2)\\ \\6x+6+3x=4x^2+4x\\ \\-4x^2+9x-4x+6=0\\ \\-4x^2+5x+6=0\ \ \ \Rightarrow\ \ \Delta=5^2-4\cdot(-4)\cdot6=25+96=121\\ \\[/tex]

[tex]x_1= \frac{-5- \sqrt{121} }{2\cdot (-4)}= \frac{-5-11}{-8} = \frac{-16}{-8} =2\ \ \ is\ integer\\ \\x_2= \frac{-5+ \sqrt{121} }{2\cdot (-4)}= \frac{-5+11}{-8} = \frac{6}{-8} =- \frac{3}{4} \ \ \ is\ not\ the\ integer[/tex]
Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.