Advertisements
Advertisements
Question
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
Solution
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
⇒ `(x - 10 + x + 6)/((x + 6)(x - 10)) = (3)/(x - 4)`
⇒ `(2x - 4)/((x + 6)(x - 10)) = (3)/(x - 4)`
⇒ (2x - 4)(x - 4) = 3 (x + 6)(x - 10)
⇒ 2x2 - 8x - 4x + 16 = 3(x2 - 4x - 60)
⇒ 2x2 - 8x - 4x + 16 = 3x2 - 12x - 180
⇒ 2x2 - 12x + 16 - 3x2 + 12x + 180 = 0
⇒ -x2 + 196 = 0
⇒ x2 - 196 = 0
⇒ (x)2 - (14)2 = 0
⇒ (x + 14)(x - 14) = 0
Either x + 14 = 0,
then x = -14
or
x - 14 = 0,
then x = 14
∴ x = 14, -14.
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
`2x^2 – x + 1/8 = 0`
Solve each of the following equations by factorization:
`x=(3x+1)/(4x)`
Two natural number differ by 3 and their product is 504. Find the numbers.
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
If 2 is a root of the equation x2 + bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =
Solve equation using factorisation method:
x(x – 5) = 24
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey
Solve the following equation by factorization
6p2+ 11p – 10 = 0
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
