Advertisements
Advertisements
Question
Find x from the following equations : `(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`
Solution
`(sqrt(12x + 1) + sqrt(2x - 3))/(sqrt(12x + 1) - sqrt(2x - 3)) = (3)/(2)`
Applying componendo and dividendo,
`(sqrt(12x + 1) + sqrt(2x - 3) + sqrt(12x + 1) - sqrt(2x - 3))/(sqrt(2x + 1) + sqrt(2x - 3) - sqrt(12x + 1) + sqrt(2x - 3)) = (3 + 2)/(3 - 2)`
⇒ `(2sqrt(12x + 1))/(2sqrt(2x - 3)) = (5)/(1)`
⇒ `(sqrt(12x + 1))/(sqrt(2x - 3)) = (5)/(1)`
Squaring both sides,
`(12x + 1)/(2x - 3) = (25)/(1)`
⇒ 50x – 75 = 12x + 1
⇒ 50x – 12x = 1 + 75
⇒ 38x = 76
⇒ x = `(76)/(38)` = 2
∴ x = 2.
APPEARS IN
RELATED QUESTIONS
If a : b = c : d, prove that: 5a + 7b : 5a – 7b = 5c + 7d : 5c – 7d.
If a : b = c : d, prove that: (9a + 13b)(9c – 13d) = (9c + 13d)(9a – 13b).
If `(a - 2b - 3c + 4d)/(a + 2b - 3c - 4d) = (a - 2b + 3c - 4d)/(a + 2b + 3c + 4d)`, show that: 2ad = 3bc.
If 7x – 15y = 4x + y, find the value of x : y. Hence, use componendo and dividendo to find the values of:
`(9x + 5y)/(9x - 5y)`
If a : b :: c : d :: e : f, then prove that `("ae" + "bf")/("ae" - "bf")` = `("ce" + "df")/("ce" - "df")`
If `(8a - 5b)/(8c - 5d) = (8a + 5b)/(8c + 5d), "prove that" a/b = c/d.`
If `a/b = c/d,` show that (9a + 13b) (9c - 13d) = (9c + 13b) (9a - 13d).
If a : b : : c : d, prove that `(5a + 11b)/(5c + 11d) = (5a - 11b)/(5c - 11d)`
If (4a + 5b) (4c – 5d) = (4a – 5d) (4c + 5d), prove that a, b, c, d are in proporton.
If x = `(sqrt(a + 1) + sqrt(a - 1))/(sqrt(a + 1 - sqrt(a - 1)`, using properties of proportion, show that x2 – 2ax + 1 = 0
