Advertisements
Advertisements
प्रश्न
Using properties of proportion, solve for x:
`(sqrt(x + 5) + sqrt(x - 16))/(sqrt(x + 5) - sqrt(x - 16)) = 7/3`
उत्तर
`(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
संबंधित प्रश्न
If p, q and r in continued proportion, then prove the following:
(p + q + r )(p - q + r) = p2 + q2 + r2
Find the mean proportion of: 5 and 80
Determine if the following numbers are in proportion:
32, 48, 70, 210
Find the value of x in each of the following proportions:
x : 92 : : 87 : 116
The 1st, 3rd, and 4th terms of a proportion are 12, 8, and 14 respectively. Find the 2nd term.
If a, b, c and d are in proportion, prove that: `abcd [(1/a^2 + 1/b^2 + 1/c^2 + 1/d^2]` = a2 + b2 + c2 + d2
If a, b, c, d are in continued proportion, prove that: `(a^3 + b^3 + c^3)/(b^3 + c^3 + d^3) = a/d`
Choose the correct answer from the given options :
The fourth proportional to 3, 4, 5 is
Write the mean and extreme terms in the following ratios and check whether they are in proportion.
78 litre is to 130 litre and 12 bottles is to 20 bottles
Determine if the following are in proportion.
33, 44, 75, 100
