Advertisements
Advertisements
Question
Solve the following equation by factorization
`(2)/(3)x^2 - (1)/(3)x` = 1
Advertisements
Solution
`(2)/(3)x^2 - (1)/(3)x` = 1
⇒ 2x2 - x = 3
⇒ 2x2 - x - 3 = 0
⇒ 2x2 - 3x + 2x - 3 = 0
⇒ x(2x - 3) + 1(2x - 3) = 0
⇒ (2x - 3) (x + 1) = 0
Either 2x - 3 = 0,
then 2x = 3
⇒ x = `(3)/(2)`
or
x + 1 = 0,
then x = -1
Hence x = `(3)/(2)`, -1.
APPEARS IN
RELATED QUESTIONS
Find the roots of the following quadratic equation by factorisation:
`sqrt2 x^2 +7x+ 5sqrt2 = 0`
Solve the following quadratic equations by factorization:
6x2 - x - 2 = 0
Solve the following quadratic equations by factorization:
`3x^2-2sqrt6x+2=0`
Find the consecutive numbers whose squares have the sum 85.
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
Solve for x:
4x2 + 4bx − (a2 − b2) = 0
If x = 1 is a common roots of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
Solve the following equation by factorisation :
`sqrt(3x^2 - 2x - 1) = 2x - 2`
