Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
Advertisements
उत्तर
We have been given
`1/(x-2)+2/(x-1)=6/x`
x2 - x + 2x2 - 4x = 6(x2 - x - 2x + 2)
3x2 - 13x + 12 = 0
3x2 - 9x - 4x + 12 = 0
3x(x - 3) - 4(x - 3) = 0
(3x - 4)(x - 3) = 0
Therefore,
3x - 4 = 0
3x = 4
x = 4/3
Or,
x - 3 = 0
x = 3
Hence, x = 4/3 or x = 3
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations
(i) x2 + 5x = 0 (ii) x2 = 3x (iii) x2 = 4
A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of toys produced in a day. On a particular day, the total cost of production was Rs 750. We would like to find out the number of toys produced on that day.
Solve the following quadratic equations by factorization:
`(x-1/2)^2=4`
The sum of the squares of two consecutive positive even numbers is 452. Find the numbers.
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
Solve equation using factorisation method:
`(x - 3)/(x + 3) + (x + 3)/(x - 3) = 2 1/2`
Car A travels x km for every litre of petrol, while car B travels (x + 5) km for every litre of petrol.
If car A use 4 litre of petrol more than car B in covering the 400 km, write down and equation in x and solve it to determine the number of litre of petrol used by car B for the journey.
Solve the following equation by factorization
`(x^2 - 5x)/(2)` = 0
Solve the following equation by factorization
x (2x + 1) = 6
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
The hypotenuse of grassy land in the shape of a right triangle is 1 metre more than twice the shortest side. If the third side is 7 metres more than the shortest side, find the sides of the grassy land.
Solve the following equation by factorisation :
`sqrt(x + 15) = x + 3`
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
If 'p' is a root of the quadratic equation x2 – (p + q) x + k = 0, then the value of 'k' is ______.
If x4 – 5x2 + 4 = 0; the values of x are ______.
