Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation view all coursesPage 2Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts Dedicated counsellor for each student Detailed Performance Evaluation Sum of two numbers is 16. The sum of their reciprocals is 1/3. Find the numbers. Given that the sum of two numbers is 16. Let the two numbers be x and 16 - x By the given hypothesis, we have `rArr1/x+1/(16-x)=1/3` `rArr(16-x+x)/(x(16-x))=1/3` ⇒ 48 = 16x - x2 ⇒ 𝑥2 - 16𝑥 + 48 = 0 ⇒ 𝑥2 - 12𝑥 - 4𝑥 + 48 = 0 ⇒ x(x - 12) - 4(x - 12) = 0 ⇒ (x - 12) (x - 4) = 0 ⇒ x = 12 or x = 4 ∴ The two numbers are 4 and 12. Concept: Solutions of Quadratic Equations by Factorization Is there an error in this question or solution? |