Advertisements
Advertisements
Question
Find x in terms of a, b and c: `a/(x-a)+b/(x-b)=(2c)/(x-c)`
Advertisements
Solution
Consider the given equation:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
Taking the LCM and then cross multiplying, we get
`(a(x-b)+b(x-a))/((x-a)(x-b))=(2c)/(x-c)`
⇒(x−c)[a(x−b)+b(x−a)]=2c(x−a)(x−b)
⇒(x−c)[ax−ab+bx−ab]=2c(x2−bx−ax+ab)
⇒ax2−2abx+bx2−acx+2abc−bcx=2cx2−2bcx−2acx+2abc
⇒ax2+bx2−2cx2=2abx−acx−bcx
⇒(a+b−2c)x2=x(2ab−ac−bc)
⇒(a+b−2c)x2−x(2ab−ac−bc)=0
⇒x[(a+b−2c)x−(2ab−ac−bc)]=0
⇒x=0 or (a+b−2c)x−(2ab−ac−bc)=0
⇒x=0 or (a+b−2c)x=(2ab−ac−bc)
`=>x = 0 `
Thus, the two roots of the given equation are x = 0 and `(2ab-ac-bc)/(a+b-2c)`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`4sqrt3x^2+5x-2sqrt3=0`
Solve the following quadratic equations by factorization:
`x^2-(sqrt3+1)x+sqrt3=0`
Solve the following quadratic equations by factorization:
`(x+3)/(x-2)-(1-x)/x=17/4`
If two pipes function simultaneously, a reservoir will be filled in 12 hours. One pipe fills the reservoir 10 hours faster than the other. How many hours will the second pipe take to fill the reservoir?
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.
