Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
Advertisements
उत्तर
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
⇒ `((x + 1)(x + 2)+ (x - 2)(x -1))/((x - 1)(x + 2)` = 3
⇒ `(x^2 + 2x + x + 2 + x^2 - x - 2x + 2)/(x^2 + 2x - x - 2)`
⇒ `(x^2 + 3x + 2 + x^2 - 3x + 2)/(x^2 + x - 2) = (3)/(1)`
⇒ 2x2 + 4 = 3x2 + 3x - 6
⇒ 2x2 + 4 - 3x2 - 3x + 6 = 0
⇒ -x2 - 3x + 10 = 0
⇒ x2 + 3x - 10 = 0
⇒ x2 + 5x - 2x - 10 = 0
⇒ x(x + 5) - 2(x + 5) = 0
⇒ (x + 5) (x - 2) = 0
Either x + 5 = 0,
then x = -5
or
x - 2 = 0,
then x = 2
Hence x = -5, 2.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equations by factorization:
3x2 = -11x - 10
The sum of a natural number and its square is 156. Find the number.
The sum of natural number and its positive square root is 132. Find the number.
Solve the following equation :
`1/(("x" - 1)(x - 2)) + 1/(("x" - 2)("x" - 3)) + 1/(("x" - 3)("x" -4)) = 1/6`
Solve the following equation by factorization
`x^2/(15) - x/(3) - 10` = 0
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
If the perimeter of a rectangular plot is 68 m and the length of its diagonal is 26 m, find its area.
A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
