Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
उत्तर
We have been given,
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
a(x - b)(x - c) + b(x - a)(x - c) = 2c(x - a)(x - b)
a(x2-(b + c)x + bc) + b(x2 - (a + c)x + ac) = 2c(x2 - (a + b)x + ab)
(a + b - 2c)x2 - (2ab - ac - bc)x = 0
x[(a + b - 2c)x - (2ab - ac - bc)] = 0
Therefore,
x = 0
Or,
(a + b - 2c)x - (2ab - ac - bc) = 0
(a + b - 2c)x = (2ab - ac - bc)
`x=(2ab - ac - bc)/(a + b - 2c)`
Hence, x = 0 or `x=(2ab - ac - bc)/(a + b - 2c)`
APPEARS IN
संबंधित प्रश्न
The length of a hall is 5 m more than its breadth. If the area of the floor of the hall is 84 m2, what are the length and breadth of the hall?
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
(m – 3)x2 – 4x + 1 = 0
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
In the following determine the set of values of k for which the given quadratic equation has real roots: \[2 x^2 + x + k = 0\]
If ax2 + bx + c = 0 has equal roots, then c =
A two digit number is such that the product of the digits is 14. When 45 is added to the number, then the digit are reversed. Find the number.
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
The speed of a boat in still water is 15km/ hr. It can go 30km upstream and return downstream to the original point in 4 hours 30 minutes. Find the speed of the stream.
A person was given Rs. 3000 for a tour. If he extends his tour programme by 5 days, he must cut down his daily expenses by Rs. 20. Find the number of days of his tour programme.
If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than five times her actual age. What is her age now?
