Advertisements
Advertisements
प्रश्न
Solve the following equation by factorization
`(1)/(7)(3x – 5)^2`= 28
Advertisements
उत्तर
`(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
संबंधित प्रश्न
Find the roots of the following quadratic equation by factorisation:
x2 – 3x – 10 = 0
The sum of a number and its square is 63/4. Find the numbers.
A fast train takes one hour less than a slow train for a journey of 200 km. If the speed of the slow train is 10 km/hr less than that of the fast train, find the speed of the two trains.
A train covers a distance of 90 km at a uniform speed. Had the speed been 15 km/hour more, it would have taken 30 minutes less for a journey. Find the original speed of the train.
Solve the following equation: 4x2 + 16x = 0
The difference of the square of two natural numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.
The length of verandah is 3m more than its breadth. The numerical value of its area is equal to the numerical value of its perimeter.
(i) Taking x, breadth of the verandah write an equation in ‘x’ that represents the above statement.
(ii) Solve the equation obtained in above and hence find the dimension of verandah.
In each of the following determine whether the given values are solutions of the equation or not.
6x2 - x - 2 = 0; x = `-(1)/(2), x = (2)/(3)`
In each of the following, determine whether the given values are solution of the given equation or not:
x2 - 3`sqrt(3)` + 6 = 0; x = `sqrt(3)`, x = -2`sqrt(3)`
A two digit positive number is such that the product of its digits is 6. If 9 is added to the number, the digits interchange their places. Find the number.
