Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`a/(x-a)+b/(x-b)=(2c)/(x-c)`
Advertisements
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
Solve the following quadratic equations by factorization:
3x2 − 14x − 5 = 0
The product of two successive integral multiples of 5 is 300. Determine the multiples.
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
`x^2+8x-2=0`
The sum of the squares to two consecutive positive odd numbers is 514. Find the numbers.
Find the two consecutive positive even integers whose product is 288.
Solve the following quadratic equations by factorization:
\[\frac{4}{x} - 3 = \frac{5}{2x + 3}, x \neq 0, - \frac{3}{2}\]
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
If y = 1 is a common root of the equations \[a y^2 + ay + 3 = 0 \text { and } y^2 + y + b = 0\], then ab equals
The sum of a number and its reciprocal is `2 9/40`. Find the number.
A two digit number is such that the product of its digit is 8. When 18 is subtracted from the number, the digits interchange its place. Find the numbers.
There is a square field whose side is 44m. A square flower bed is prepared in its centre leaving a gravel path all round the flower bed. The total cost of laying the flower bed and graving the path at Rs 2. 75 and Rs. 1.5 per square metre, respectively, is Rs 4,904. Find the width of the gravel path.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization
`x + (1)/x = 2(1)/(20)`
Is 0.2 a root of the equation x2 – 0.4 = 0? Justify
