Advertisements
Advertisements
प्रश्न
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Advertisements
उत्तर
`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
संबंधित प्रश्न
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
`7x^2+3x-4=0`
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Find the values of k for which the roots are real and equal in each of the following equation:\[px(x - 3) + 9 = 0\]
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
Find two consecutive integers such that the sum of their squares is 61
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
If x = 3 is one root of the quadratic equation 2x2 + px + 30 = 0, find the value of p and the other root of the quadratic equation.
