Advertisements
Advertisements
Question
Solve the following equation by factorization
`x/(x + 1) + (x + 1)/x = (34)/(15)`
Advertisements
Solution
`x/(x + 1) + (x + 1)/x = (34)/(15)`
`(x^2 + x^2 + 2x + 1)/(x(x + 1)) = (34)/(15)`
⇒ `(2x^2 + 2x + 1)/(x^2 + x) = (34)/(15)`
⇒ 30x2 + 30x + 15 = 34x2 + 34x
⇒ 30x2 + 30x + 15 - 34x2 - 34x = 0
⇒ -4x2 - 4x + 15 = 0
⇒ 4x2 + 4x - 15 = 0
⇒ 4x2 + 10x - 6x - 15 = 0
⇒ 2x(2x + 5) - 3(2x + 5) = 0
⇒ (2x + 5) (2x - 3) = 0
Either 2x + 5 = 0,
then 2x = -5
⇒ x = `(-5)/(2)`
or
2x - 3 = 0,
then 2x = 3
⇒ x = `(3)/(2)`
Hence x = `(-5)/(2), (3)/(2)`.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
(2x + 3)(3x − 7) = 0
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
The sum of two natural numbers is 15 and the sum of their reciprocals is `3/10`. Find the numbers.
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
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 present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
If an integer is added to its square the sum is 90. Find the integer with the help of a quadratic equation.
Solve the following equation by factorization
3x2= x + 4
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
