Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
`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`
⇒`(5x + 30 - 3x + 6)/(x^2 + 6x - 2x - 12) = 4/x`
⇒ `(2x + 36)/(x^2 + 4x - 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 equations by factorization:
6x2 + 11x + 3 = 0
Solve the following quadratic equations by factorization:
`1/(x-1)-1/(x+5)=6/7` , x ≠ 1, -5
Find the whole numbers which when decreased by 20 is equal to 69 times the reciprocal of the members.
The area of a right angled triangle is 165 m2. Determine its base and altitude if the latter exceeds the former by 7 m.
Find two consecutive multiples of 3 whose product is 648.
Solve equation using factorisation method:
x(x – 5) = 24
Solve equation using factorisation method:
`x = (3x + 1)/(4x)`
Solve the following equation and give your answer up to two decimal places:
x2 − 5x − 10 = 0
Solve the following equation by factorization
3(x – 2)2 = 147
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.
