JEE Exam > JEE Questions > If x1 and x2 are the two values of x satisfyi...
Start Learning for Free
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2?
Most Upvoted Answer
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2...
Solving the given equation using substitution:
Let a = 7^(x^2)
Then the equation becomes a^2 - 2(a*7^x*sqrt(3x)) + 7^(24) = 0
Using quadratic formula, we get:
a = [2(7^x*sqrt(3x)) ± sqrt(4(7^(2x)*3x) - 4(7^24))]/2
a = 7^x*sqrt(3x) ± sqrt(7^(2x)*3x - 7^24)
Substituting back to find x1 and x2:
Since a = 7^(x^2), we can substitute back to get:
7^(x^2) = 7^x*sqrt(3x) + sqrt(7^(2x)*3x - 7^24) or 7^x*sqrt(3x) - sqrt(7^(2x)*3x - 7^24)
Taking the natural logarithm of both sides and simplifying, we get:
x^2 = x*log(7) + 1/2*log(3x) ± 1/2*log(7^(2x)*3x - 7^24)
This can be solved using numerical methods or graphing to find the solutions x1 and x2.
Final Answer:
The values of x1 and x2 depend on the exact form of the expression in the last equation, which is difficult to simplify further. Therefore, numerical methods or graphing must be used to find the solutions.
Let a = 7^(x^2)
Then the equation becomes a^2 - 2(a*7^x*sqrt(3x)) + 7^(24) = 0
Using quadratic formula, we get:
a = [2(7^x*sqrt(3x)) ± sqrt(4(7^(2x)*3x) - 4(7^24))]/2
a = 7^x*sqrt(3x) ± sqrt(7^(2x)*3x - 7^24)
Substituting back to find x1 and x2:
Since a = 7^(x^2), we can substitute back to get:
7^(x^2) = 7^x*sqrt(3x) + sqrt(7^(2x)*3x - 7^24) or 7^x*sqrt(3x) - sqrt(7^(2x)*3x - 7^24)
Taking the natural logarithm of both sides and simplifying, we get:
x^2 = x*log(7) + 1/2*log(3x) ± 1/2*log(7^(2x)*3x - 7^24)
This can be solved using numerical methods or graphing to find the solutions x1 and x2.
Final Answer:
The values of x1 and x2 depend on the exact form of the expression in the last equation, which is difficult to simplify further. Therefore, numerical methods or graphing must be used to find the solutions.
Community Answer
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2...
69
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Similar JEE Doubts
Top Courses for JEEView all
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2?
Question Description
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2?.
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2?.
Solutions for If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? defined & explained in the simplest way possible. Besides giving the explanation of
If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2?, a detailed solution for If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? has been provided alongside types of If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? theory, EduRev gives you an
ample number of questions to practice If x1 and x2 are the two values of x satisfying the equation 7^(2(x)^2) - 2(7^(x)^2 +12x) +7^(2x +24) =0 then find x1+ x2? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup