LIVE Course for free

Rated by 1 million+ students
Get app now
0 votes
17 views
in Aptitude by (30.0k points)
closed by

If (x4) + (1/x4) = 674, then find the value of x.


1. 2√7
2. 2√6 + 2√7
3. √6 + √7
4. 2√6
5. 4√6 + √7

1 Answer

0 votes
by (54.3k points)
selected by
 
Best answer
Correct Answer - Option 3 : √6 + √7

Given:

(x4) + (1/x4) = 674 

Formula Used:

(x4) + (1/x4) = k, then (x2) + (1/x2) = √(k + 2)

(x2) + (1/x2) = m, then (x) + (1/x) = √(m + 2)

(x2) + (1/x2) = m, then (x) - (1/x) = √(m - 2)

Calculation:

(x4) + (1/x4) = 674

Then,

(x2) + (1/x2) = √(674 + 2)

⇒ (x2) + (1/x2) = √676

⇒ (x2) + (1/x2) = 26

Now,

(x) + (1/x) = √(26 + 2)

⇒ (x) + (1/x) = √28

⇒ (x) + (1/x) = 2√7     ...(i)

And,

(x) - (1/x) = √(26 - 2)

⇒ (x) - (1/x) = √24

⇒ (x) - (1/x) = 2√6     ...(ii)

Adding equation i and ii

[(x) + (1/x)] + [(x) - (1/x)] = 2√7 + 2√6

⇒ 2x = 2(√7 + √6)

⇒ x = (√7 + √6)

The value of x is (√7 + √6)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...