If a = 3 + 2√2, then find the value of (a6 – a4 – a2 + 1)/a3.

  1. 198
  2. 204
  3. 192
  4. 210

Answer (Detailed Solution Below)

Option 3 : 192
ssc-cgl-crash
Free
PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
1.9 Lakh Users
25 Questions 50 Marks 20 Mins

Detailed Solution

Download Solution PDF

Given:

a = 3 + 2√2

Concept Used:

a2 – b2 = (a – b)(a + b)

a3 + b3 = (a + b)3 – 3ab(a + b)

Calculation:

a = 3 + 2√2

1/a = 1/(3 + 2√2)

⇒ 1/a = (3 – 2√2)/{(3 + 2√2) × (3 – 2√2)}

⇒ 1/a = (3 – 2√2)/{32 – (2√2)2}

⇒ 1/a = (3 – 2√2)/(9 – 8)

⇒ 1/a = (3 – 2√2)

Now,

a + 1/a = 3 + 2√2 + 3 – 2√2

⇒ a + 1/a = 6

(a6 – a4 – a2 + 1)/a3

⇒ a3 – a – 1/a + 1/a3

⇒ (a3 + 1/a3) – (a + 1/a)

⇒ {(a + 1/a)3 – 3(a + 1/a)} – (a + 1/a)

⇒ (63 – 3 × 6) – 6

⇒ 216 – 18 – 6

⇒ 192

The required value of (a6 – a4 – a2 + 1)/a3 is 192

Latest SSC CGL Updates

Last updated on Jun 9, 2025

-> The SSC CGL Notification 2025 has been released on 9th June 2025 at ssc.gov.in.

-> The SSC CGL exam registration process is now open and will continue till 4th July 2025, so candidates must fill out the SSC CGL Application Form 2025 before the deadline.

-> This year, the Staff Selection Commission (SSC) has announced approximately 14,582 vacancies for various Group B and C posts across government departments.

->  The SSC CGL Tier 1 exam is scheduled to take place from 13th to 30th August 2025.

->  Aspirants should visit ssc.gov.in 2025 regularly for updates and ensure timely submission of the SSC CGL exam form.

-> Candidates can refer to the SSC CGL syllabus for a better understanding of the exam structure and pattern.

-> The SSC CGL Eligibility is a bachelor’s degree in any discipline.

-> Candidates selected through the SSC CGL exam will receive an attractive salary. Learn more about the SSC CGL Salary Structure.

-> Attempt SSC CGL Free English Mock Test and SSC CGL Current Affairs Mock Test.

-> Candidates should also use the SSC CGL previous year papers for a good revision. 

Get Free Access Now
Hot Links: teen patti master game teen patti rules teen patti joy