Advertisements
Advertisements
Question
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
Advertisements
Solution
`(1)/(7)(3x – 5)^2`= 28
(3x – 5)2 = 28 × 7
⇒ 9x2 – 30x + 25 = 196
⇒ 9x2 - 30x + 25 - 196 = 0
⇒ 9x2 - 30x - 171 = 0
⇒ 3x2 - 10x - 57 = 0
⇒ 3x2 - 19x + 9x - 57 = 0
⇒ x(3x - 19) + 3 (3x - 19) = 0
⇒ (3x - 19) (x + 3) = 0
Either 3x - 19 = 0,
then 3x = 19
⇒ x = `(19)/(3)`
or
x + 3 = 0,
then x = -3
Hence x = `(19)/(3)`, -3.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equation by Factorisation method: x2 + 7x + 10 = 0
Solve the following quadratic equations by factorization:
`(2x)/(x-4)+(2x-5)/(x-3)=25/3`
Solve the following quadratic equations by factorization:
a(x2 + 1) - x(a2 + 1) = 0
The sum of two numbers is 48 and their product is 432. Find the numbers?
Two number differ by 4 and their product is 192. Find the numbers?
Solve the following quadratic equation by factorisation.
`sqrt2 x^2 + 7x + 5sqrt2 = 0` to solve this quadratic equation by factorisation, complete the following activity.
`sqrt2 x^2 + 7x + 5sqrt2 = 0`
`sqrt2x^2+square+square+5sqrt2=0`
`x("______") + sqrt2 ("______") = 0`
`("______") (x + sqrt2) = 0`
`("______") = 0 or (x + sqrt2) = 0`
∴ x = `square or x = -sqrt2`
∴ `square` and `-sqrt(2)` are roots of the equation.
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
The polynomial equation x(x + 1) + 8 = (x + 2) (x – 2) is:
Find the roots of the following quadratic equation by the factorisation method:
`2x^2 + 5/3x - 2 = 0`
If the area of a square is 400 m2, then find the side of the square by the method of factorization.
