Advertisements
Advertisements
प्रश्न
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
Advertisements
उत्तर
`"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
`("a"("x" - "b") + "b"("x" - "a"))/(("x" - "a")("x" - "b")) = (2"c")/("x" - "c")`
`("ax - ab + bx - ab")/("x"^2 - "ax" - "bx" + "ab") = (2"c")/("x" - "c")`
`(("a + b")"x" - 2 "ab")/("x"^2 - ("a + b")"x" + "ab") = (2"c")/("x" - "c")`
{(a+ b) x- 2ab} (x- c) = 2c {x2 - (a + b) x + ab}
(a+ b )x2 - 2abx - c (a+ b )x + 2abc = 2cx2 - 2c( a+ b )x + 2abc
(a+ b )x2 - [2ab + c( a+ b )]x + 2abc = 2cx2 - 2c( a+ b )x + 2abc
(a+ b-2c)x2 = (2ab + ac+ bc- 2ca - 2bc)x
(a+ b-2c )x2 = (2ab - ac - bc) x
x = 0 , x = `(2"ab" - "ac" - "bc")/("a" + "b" - 2"c")`
APPEARS IN
संबंधित प्रश्न
The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve each of the following equations by factorization:
`9/2x=5+x^2`
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
the return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
Solve the equation:
`6(x^2 + (1)/x^2) -25 (x - 1/x) + 12 = 0`.
In each of the following determine whether the given values are solutions of the equation or not.
3x2 - 2x - 1 = 0; x = 1
Solve the following equation by factorization
`x + (1)/x = 2(1)/(20)`
Find the roots of the following quadratic equation by the factorisation method:
`21x^2 - 2x + 1/21 = 0`
At present Asha’s age (in years) is 2 more than the square of her daughter Nisha’s age. When Nisha grows to her mother’s present age, Asha’s age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
