Advertisements
Advertisements
Question
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Advertisements
Solution
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
`(("x" -3)("x" - 4) + ("x" - 1)("x" - 4) + ("x" - 1)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`("x"^2 - 3"x" - 4"x" + 12 + "x"^2 - "x" - 4"x" + 4 + "x"^2 - "x" - 2"x" + 2)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3"x"^2 - 15 "x" + 18)/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3("x"^2 - 5"x" + 6))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`(3("x" - 3)("x" - 2))/(("x" - 1)("x" - 2)("x" - 3)("x" - 4)) = 1/6`
`3/(("x" - 1)("x" - 4)) = 1/6`
x2 - 5x+ 4= 18
x2 - 5x - 14= 0
x2 + 2x - 7x -14= 0
x( x+ 2) - 7(x + 2)= 0
(x + 2)(x - 7) = 0
x = -2, x = 7
APPEARS IN
RELATED QUESTIONS
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
The distance between Akola and Bhusawal is 168 km. An express train takes 1 hour less than a passenger train to cover the distance. Find the average speed of each train if the average speed of the express train is more by 14 km/hr than the speed of the passenger train.
The number of quadratic equations having real roots and which do not change by squaring their roots is
Solve the following equation: `10"x" - 1/"x" = 3`
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
The sum of the square of 2 positive integers is 208. If the square of larger number is 18 times the smaller number, find the numbers.
Divide 16 into two parts such that the twice the square of the larger part exceeds the square of the smaller part by 164.
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
The roots of the equation x2 + 3x – 10 = 0 are ______.
