Advertisements
Advertisements
Question
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Solution
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
Applying componendo and dividendo,
`(sqrt(x + 5)+ sqrt(x - 16) + sqrt(x + 5) - sqrt(x - 16))/(sqrt(x + 5)+sqrt(x - 16) - sqrt(x + 5) + sqrt(x -16)) = (7 + 3)/(7 - 3)`
`(2sqrt(x + 5))/(2sqrt(x - 16)) = 10/4`
`sqrt(x + 5)/sqrt(x - 16) = 5/2`
Squaring both sides,
`(x + 5)/(x - 16) = 25/4`
4x + 20 = 25x – 400
21x = 420
`x = 420/21 = 20`
APPEARS IN
RELATED QUESTIONS
Find mean proportional of `( x + y)/( x - y), (x^2 - y^2)/(x^2y^2)`
What quantity must be added to each term of the ratio a + b: a - b to make it equal to (a + b)2 : (a - b)2 ?
Find the two numbers such that their mean proprtional is 24 and the third proportinal is 1,536.
Determine if the following numbers are in proportion:
32, 48, 70, 210
Verify the following:
91 : 104 : : 119 : 136
If Rs 760 is divided between A and B in the ratio 8 : 11, then B's share is
10 books is to 15 books as 3 books is to 15 books
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
400 gm is to 50 gm and 25 rupees is to 625 rupees
If b : a = c : d, then a, b, c, d are in proportion.
Are the following statements true?
45 km : 60 km = 12 hours : 15 hours
