Advertisements
Advertisements
Questions
Using properties of proportion, solve for x. Given that x is positive:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Using properties of proportion, find the value of x from the following:
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
Advertisements
Solution
`(2x + sqrt(4x^2 -1))/(2x - sqrt(4x^2 - 1)) = 4`
⇒ `(2x + sqrt(4x^2 -1) + 2x - sqrt(4x^2 - 1))/(2x + sqrt(4x^2 - 1) - 2x + sqrt(4x^2 - 1)) = (4+1)/(4-1) ` (By componendo dividendo)
⇒ `(4x)/(2sqrt(4x^2 -1)) = 5/3`
⇒ `(2x)/(sqrt(4x^2 -1)) = 5/3`
Squaring both sides,
⇒ `((2x)/sqrt(4x^2 - 1))^2 = (5/3)^2`
⇒ `(4x^2)/(4x^2 -1) = 25/9`
⇒ 9(4x2) = 25(4x2 − 1)
⇒ 36x2 = 100x2 − 25
⇒ 64x2 = 25
⇒ x2 = `25/64`
⇒ x = `5/8`
APPEARS IN
RELATED QUESTIONS
If x, y, z are in continued proportion, prove that `(x + y)^2/(y + z)^2 = x/z`
If a, b, c and dare in continued proportion, then prove that
ad (c2 + d2) = c3 (b + d)
If a, b, c and dare in continued proportion, then prove that
(a+ d)(b+ c)-(a+ c)(b+ d)= (b-c)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 ?
If a, b, c, d are in continued proportion, prove that:
`sqrt(ab) - sqrt(bc) + sqrt(cd) = sqrt((a - b + c) (b - c + d)`
Write (T) for true and (F) for false in case of the following:
81 kg : 45 kg : : 18 men : 10 men
If y is mean proportional between x and z, prove that xyz (x + y + z)³ = (xy + yz + zx)³.
If a, b, c are in continued proportion, prove that: `(pa^2+ qab+ rb^2)/(pb^2+qbc+rc^2) = a/c`
Choose the correct answer from the given options :
If x, 12, 8 and 32 are in proportion, then the value of x is
10 g of caustic soda dissolved in 100 mL of water makes a solution of caustic soda. Amount of caustic soda needed for 1 litre of water to make the same type of solution is ______.
