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
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
A two digit number is 4 times the sum of its digits and twice the product of its digits. Find the number.
If one root the equation 2x2 + kx + 4 = 0 is 2, then the other root is
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
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.
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
Find two consecutive even natural numbers such that the sum of their squares is 340.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
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.
