Advertisements
Advertisements
Question
Solve the following equation: `(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
Advertisements
Solution
`(2"x")/("x" - 4) + (2"x" - 5)/("x" - 3) = 25/3`
`(6 "x")/("x" - 4) + (6"x" - 15)/("x" - 3) = 25`
6x (x- 3)+ (6x- 15) (x- 4) = 25 (x- 4) (x-3)
6x2 -18x + 6x2 - 15x - 24x + 60 = 25 (x2 - 4x - 3x + 12)
12x2 - 57x + 60 = 25x2 - 175 x + 300
13x2 - 118 x + 240 = 0
`"x"^2 - 118/13 "x" + 240/13 = 0`
`"x"^2 - 6"x" - 40/13 "x" + 240/13 = 0`
`"x" ("x" - 6) - 40/13 ("x" - 6) = 0`
`("x" + 6)("x" - 40/13) = 0`
x = 6 , x = `40/13`
APPEARS IN
RELATED QUESTIONS
Solve the equation:`14/(x+3)-1=5/(x+1); xne-3,-1` , for x
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
Divide 29 into two parts so that the sum of the squares of the parts is 425.
The perimeter of a rectangular field is 82 m and its area is 400 m2. Find the breadth of the rectangle.
The sum of the squares two consecutive multiples of 7 is 1225. Find the multiples.
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Determine whether the values given against the quadratic equation are the roots of the equation.
2m2 – 5m = 0, m = 2, `5/2`
Two pipes flowing together can fill a cistern in 6 minutes. If one pipe takes 5 minutes more than the other to fill the cistern, find the time in which each pipe would fill the cistern.
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
