Question
If (x + 6y) = 8, and xy = 2, where x > 0, what is the
value of (x3 + 216y³)?Solution
xy = 2 ⇒ y = 2/x .....(1) Also, (x + 6y) = 8 ⇒ x + (6 × 2/x) = 8 ⇒ x + 12/x = 8 .....(2) ⇒ (x + 12/x)3 = 83 [Taking cube of both sides] ⇒ x3 + (12/x)3 + 3 × x × (12/x) (x + 12/x) 512 ⇒ x3 + (12/x)3 + 3 × 12 × 8 = 512 [∵ We get from equation (2), x + 12/x = 8] ⇒ x3 + (12/x)3 + 288 = 512 ⇒ x3 + (12/x)3 = 512 - 288 ⇒ x3 + [(2 × 6)/x]3 = 224 ⇒ x3 + (6y)3 = 224 [∵ y = 2/x] ⇒ x3 + 216y3 = 224 ∴ The value of x3 + 216y3 is 224
Who finished second in the SuperUnited Rapid and Blitz 2025 chess tournament?
As per the National Education Policy, 2020, which of the following National Curriculum Framework (NCF) will be developed?
1. National Curriculum ...
Which company recently secured a Rs 13,300 crore order from Damodar Valley Corporation (DVC) to set up a 1600 MW (2X800MW) thermal power plant in Koderm...
Which of the following information is incorrect with respect to the payroll data provided by the Employees' Provident Fund Organisation-
I.New mo...
Which clothing brand collaborated with the National Basketball Association (NBA) to launch and operate NBAStore.in in India?
Which platform type is exempt from the Australian social media ban for under-16s?
What is the transaction capacity of the new UPI Switch infrastructure developed by Razorpay?
As per the Reserve Bank of India (RBI) report, what percentage of global real-time payment volumes does India account for?
By which date is the Telangana government aiming to roll out the Bhu Bharati portal across the state?
Which of the following statements accurately reflects the approvals granted by the Competition Commission of India (CCI) in July 2024?
A) Transac...
Relevant for Exams:
