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 for x
`(x - 1)/(2x + 1) + (2x + 1)/(x - 1) = 2, "where x" != -1/2, 1`
If the quadratic equation (c2 – ab) x2 – 2 (a2 – bc) x + b2 – ac = 0 in x, has equal roots, then show that either a = 0 or a3 + b3 + c3 = 3abc ?
Determine whether the values given against the quadratic equation are the roots of the equation.
x2 + 4x – 5 = 0 , x = 1, –1
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
A two digit number is such that the product of the digits is 12. When 36 is added to this number the digits interchange their places. Determine the number.
Solve the following by reducing them to quadratic equations:
`((7y - 1)/y)^2 - 3 ((7y - 1)/y) - 18 = 0, y ≠ 0`
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
Solve the following quadratic equation by factorisation method:
x2 + x – 20 = 0
Find the roots of the quadratic equation x2 – x – 2 = 0.
