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:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Solve the following quadratic equations by factorization:
`(3x-2)/(2x-3)=(3x-8)/(x+4)`
If \[x = - \frac{1}{2}\],is a solution of the quadratic equation \[3 x^2 + 2kx - 3 = 0\] ,find the value of k.
Solve the following equation :
`sqrt 2 "x"^2 - 3"x" - 2 sqrt 2 = 0`
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
In each of the following determine whether the given values are solutions of the equation or not
2x2 - 6x + 3 = 0; x = `(1)/(2)`
Which of the following are the roots of the quadratic equation, x2 – 9x + 20 = 0 by factorisation?
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
If α and β are roots of the quadratic equation x2 – 7x + 10 = 0, find the quadratic equation whose roots are α2 and β2.
