Question
Download Solution PDFIf \(\frac{{\left( {{\rm{15x - 9}}} \right)}}{{\rm{x}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15y - 9}}} \right)}}{{\rm{y}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15z - 9}}} \right)}}{{\rm{z}}}\) = 0, then the value of \(\frac{{\rm{1}}}{{\rm{x}}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{y}}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{z}}}\) is :
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
\(\frac{{\left( {{\rm{15x - 9}}} \right)}}{{\rm{x}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15y - 9}}} \right)}}{{\rm{y}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15z - 9}}} \right)}}{{\rm{z}}}\)= 0
Calculation:
\(\frac{{\left( {{\rm{15x - 9}}} \right)}}{{\rm{x}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15y - 9}}} \right)}}{{\rm{y}}}\,\,{\rm{ + }}\,\,\frac{{\left( {{\rm{15z - 9}}} \right)}}{{\rm{z}}}=0\\ {(15x-9)yz + (15y-9)xz+(15z-9)xy \over xyz} = 0\\ 15xyz-9yz+15xyz-9xz+15xyz-9xy=0\\ 45xyz-9yz-9xz-9xy=0\\ 5xyz-yz-xz-xy=0\\ 5xyz=yz+xz+xy\\ 5={yz+xz+xy \over xyz}\\ {1\over x}+{1 \over y}+ {1\over z} = 5\)
Therefore, the value of \(\frac{{\rm{1}}}{{\rm{x}}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{y}}}\,{\rm{ + }}\,\frac{{\rm{1}}}{{\rm{z}}} \) is 5.
Last updated on Jul 18, 2025
-> A total of 1,08,22,423 applications have been received for the RRB Group D Exam 2025.
-> The RRB Group D Exam Date will be announced on the official website. It is expected that the Group D Exam will be conducted in August-September 2025.
-> The RRB Group D Admit Card 2025 will be released 4 days before the exam date.
-> The RRB Group D Recruitment 2025 Notification was released for 32438 vacancies of various level 1 posts like Assistant Pointsman, Track Maintainer (Grade-IV), Assistant, S&T, etc.
-> The minimum educational qualification for RRB Group D Recruitment (Level-1 posts) has been updated to have at least a 10th pass, ITI, or an equivalent qualification, or a NAC granted by the NCVT.
-> Check the latest RRB Group D Syllabus 2025, along with Exam Pattern.
-> The selection of the candidates is based on the CBT, Physical Test, and Document Verification.
-> Prepare for the exam with RRB Group D Previous Year Papers.