if x = to 4 root 6 by root 2 + root 3 then find the value of x + 2 root 2 by x minus 2 root 2 plus X + 2 root 3 by x minus 2 root 3
Answers
Given : x = 4√6 / (√2 + √3)
To find : value of (x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3)
Solution:
x = 4√6 / (√2 + √3)
multiplying & dividing by √3 - √2
=> x =4√6 ( √3 - √2)
=> x = 12√2 - 8√3
(x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3)
= (12√2 - 8√3 + 2√2)/(12√2 - 8√3 - 2√2 ) + (12√2 - 8√3 + 2√3)/(12√2 - 8√3 - 2√3 )
= (14√2 - 8√3)/(10√2 - 8√3 ) + (12√2 - 6√3)/(12√2 - 10√3 )
= (7√2 - 4√3)/(5√2 - 4√3 ) + 3(2√2 - √3)/(6√2 - 5√3 )
= (7√2 - 4√3)/(5√2 + 4√3 ) / 2 + 3(2√2 - √3)(6√2 + 5√3 )/(-3)
= (70 - 48 + 28√6 - 20√6 )/2 + (√3 - 2√2)(6√2 + 5√3 )
= (22 + 8√6)/2 + (15 - 24 + 6√6 - 10√6)
= 11 + 4√6 - 9 - 4√6
= 2
(x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3) = 2
Learn more:
If, x = [root(p+q) +root(pq)] /[root(p+q) - root(pq)] then find the value
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if X= 3-2root2 find the value of root X +1/root X and root x-1/root X p
https://brainly.in/question/17278868
Answer:
Given : x = 4√6 / (√2 + √3)
To find : value of (x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3)
Solution:
x = 4√6 / (√2 + √3)
multiplying & dividing by √3 - √2
=> x =4√6 ( √3 - √2)
=> x = 12√2 - 8√3
(x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3)
= (12√2 - 8√3 + 2√2)/(12√2 - 8√3 - 2√2 ) + (12√2 - 8√3 + 2√3)/(12√2 - 8√3 - 2√3 )
= (14√2 - 8√3)/(10√2 - 8√3 ) + (12√2 - 6√3)/(12√2 - 10√3 )
= (7√2 - 4√3)/(5√2 - 4√3 ) + 3(2√2 - √3)/(6√2 - 5√3 )
= (7√2 - 4√3)/(5√2 + 4√3 ) / 2 + 3(2√2 - √3)(6√2 + 5√3 )/(-3)
= (70 - 48 + 28√6 - 20√6 )/2 + (√3 - 2√2)(6√2 + 5√3 )
= (22 + 8√6)/2 + (15 - 24 + 6√6 - 10√6)
= 11 + 4√6 - 9 - 4√6
= 2
(x + 2√2) / (x - 2√2) + (x + 2√3)/(x - 2√3) = 2