Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`1/((x-1)(x-2))+1/((x-2)(x-3))+1/((x-3)(x-4))=1/6`
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.
Solve each of the following equations by factorization:
`2x^2-1/2x=0`
Solve each of the following equations by factorization :
`6/x=1+x`
Solve each of the following equations by factorization:
`x+1/x=2.5`
The sum of two natural numbers is 9 and the sum of their reciprocals is `1/2`. Find the numbers .
If −5 is a root of the quadratic equation\[2 x^2 + px - 15 = 0\] and the quadratic equation \[p( x^2 + x) + k = 0\] has equal roots, find the value of k.
If \[1 + \sqrt{2}\] is a root of a quadratic equation will rational coefficients, write its other root.
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
Solve the following equation: abx2 +(b2-ac) x - bc = 0
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
By increasing the speed of a car by 10 km/hr, the time of journey for a distance of 72 km. is reduced by 36 minutes. Find the original speed of the car.
Solve the following quadratic equation by factorisation:
(x - 4) (x + 2) = 0
Solve the following equation by factorization
(x – 4)2 + 52 = 132
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
Solve the following equation by factorization
`3x - (8)/x `= 2
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
