Advertisements
Advertisements
Question
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
Advertisements
Solution
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
⇒ `(5("x" + 6) -3("x" -2))/(("x" -2)("x" + 6)) = 4/"x"`
⇒ `(5"x" + 30 - 3"x" + 6)/("x"^2 + 6"x" - 2"x" - 12) = 4/"x"`
⇒ `(2"x" + 36)/("x"^2 + 4"x" - 12) = 4/"x"`
⇒ 4x2 + 16x - 48 = 2x2 + 36x
⇒ 2x2 - 20x - 48 = 0
⇒ x2 - 10x - 24 = 0
⇒ x2 - 12x + 2x - 24 = 0
⇒ x(x - 12) + 2(x - 12) = 0
⇒ (x - 12) (x + 2) = 0
If x - 12 = 0 or x + 2 = 0
then x = 12 or x = -2
RELATED QUESTIONS
Solve the following quadratic equation by factorization method: 9x2-25 = 0
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
Solve the following quadratic equations by factorization:
`(2x – 3)^2 = 49`
Two natural number differ by 3 and their product is 504. Find the numbers.
Write the set of values of k for which the quadratic equation has 2x2 + kx – 8 = 0 has real roots.
If \[\left( a^2 + b^2 \right) x^2 + 2\left( ab + bd \right)x + c^2 + d^2 = 0\] has no real roots, then
The sum of the squares of three consecutive natural numbers is 110. Determine the numbers.
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
Ritu bought a saree for Rs. 60x and sold it for Rs. (500 + 4x) at a loss of x%. Find the cost price.
