Advertisements
Advertisements
Question
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
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
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
Solve the following quadratic equations by factorization:
`1/x-1/(x-2)=3` , x ≠ 0, 2
The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.
Three consecutive positive integers are such that the sum of the square of the first and the product of other two is 46, find the integers.
Solve the following quadratic equations by factorization:
`5/(x - 2) - 3/(x + 6) = 4/x`
The sum of two natural number is 28 and their product is 192. Find the numbers.
Solve (x2 + 3x)2 - (x2 + 3x) -6 = 0.
In a P.T. display, 480 students are arranged in rows and columns. If there are 4 more students in each row than the number of rows, find the number of students in each row.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
