Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
`1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6`
Solution
We have been given,
`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-4)(x-2)(x-3))=1/6`
`(3(x^2-5x+6))/((x^2-5x+4)(x^2-5x+6))=1/6`
18 = x2 - 5x + 4
x2 - 5x - 14 = 0
x2 - 7x + 2x - 14 = 0
x(x - 7) + 2(x - 7) = 0
(x + 2)(x - 7) = 0
Therefore,
x + 2 = 0
x = -2
or,
x - 7 = 0
x = 7
Hence, x = -2 or x = 7.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation for x:
`x^2+(a/(a+b)+(a+b)/a)x+1=0`
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
4x2 + 4bx - (a2 - b2) = 0
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Solve the following quadratic equations by factorization:\[\frac{1}{x - 3} + \frac{2}{x - 2} = \frac{8}{x}; x \neq 0, 2, 3\]
In each of the following, determine whether the given values are solution of the given equation or not:
`a^2x^2 - 3abx + 2b^2 = 0; x = a/b, x = b/a`.
2x articles cost Rs. (5x + 54) and (x + 2) similar articles cost Rs. (10x – 4), find x.
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
