Advertisements
Advertisements
Question
Solve the equation using the factorisation method:
`(3x -2)/(2x -3) = (3x - 8)/(x + 4)`
Solution
`(3x -2)/(2x - 3) = (3x - 8)/(x + 4)`
⇒ (3x – 2)(x + 4) = (2x – 3)(3x – 8)
⇒ 3x2 + 12x – 2x – 8 = 6x2 – 16x – 9x + 24
⇒ 3x2 + 10x – 8 = 6x2 – 25x + 24
⇒ 3x2 – 35x + 32 = 0
⇒ 3x2 – 32x – 3x + 32 = 0
⇒ x(3x – 32) – 1(3x – 32) = 0
⇒ (x – 1)(3x – 32) = 0
If x – 1 = 0 or 3x – 32 = 0
⇒ x = 1 or x = `32/3 = 10 2/3`
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Write the set of value of k for which the quadratic equations has 2x2 + kx − 8 = 0 has real roots.
If the roots of the equations \[\left( a^2 + b^2 \right) x^2 - 2b\left( a + c \right)x + \left( b^2 + c^2 \right) = 0\] are equal, then
If a and b are roots of the equation x2 + ax + b = 0, then a + b =
Solve the following equation: `7"x" + 3/"x" = 35 3/5`
Solve the following equation : x2 + 2ab = (2a + b)x
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 return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
