Question
Download Solution PDFযদি x + 1/y = 3, y + 1/z = 2 এবং z + 1/x = 4 হয়, তাহলে xyz + 1/xyz এর মান নির্ণয় করুন।
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFগণনা:
x + 1/y = 3 ----(1)
y + 1/z = 2 ----(2)
z + 1/x = 4 ----(3)
সমীকরণটিকে যোগ করুন। (1), (2) এবং (3)
⇒ x + y + z + 1/x + 1/y + 1/z = 9 ----(4)
এখন সমীকরণটিকে গুণ করুন। (1), (2) এবং (3)
⇒ (x + 1/y) × (y + 1/z) × (z + 1/x) = 3 × 2 × 4
⇒ (xy + x/z + 1 + 1/zy)(z + 1/x) = 24
⇒ (xyz + y + x + 1/z + z + 1/x + 1/y + 1/xyz) = 24
⇒ [xyz + (1/xyz) + x + y + z + 1/x + 1/y + 1/z] = 24
⇒ xyz + 1/xyz + 9 = 24
⇒ xyz + 1/xyz = 24 – 9 = 15
∴ উত্তর হল 15
Last updated on Jun 18, 2025
-> The UPSC CDS 2 Registration Date has been extended at upsconline.gov.in. for 453 vacancies.
-> Candidates can now apply online till 20th June 2025.
-> The CDS 2 Exam will be held on 14th September 2025.
-> Attempt UPSC CDS Free Mock Test to boost your score.
-> The selection process includes Written Examination, SSB Interview, Document Verification, and Medical Examination.
-> Refer to the CDS Previous Year Papers to enhance your preparation.