Advertisements
Advertisements
Question
Solve equation using factorisation method:
4(2x – 3)2 – (2x – 3) – 14 = 0
Solution
4(2x – 3)2 – (2x – 3) – 14 = 0
Let 2x – 3 = y
Then 4y2 – y – 14 = 0
⇒ 4y2 – 8y + 7y – 14 = 0
⇒ 4y(y – 2) + 7(y – 2) = 0
⇒ (y – 2)(4y + 7) = 0
If y – 2 = 0 or 4y + 7 = 0
⇒ y = 2 or y = `(-7)/4`
⇒ 2x – 3 = 2 or 2x – 3 = `(-7)/4`
⇒ 2x = 5 or 2x = `5/4`
⇒ x = `5/2` or x = `5/8`
APPEARS IN
RELATED QUESTIONS
The speed of a boat in still water is 8 km/hr. It can go 15 km upstream and 22 km downstream in 5 hours. Find the speed of the stream.
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Solve the following quadratic equation for x:
`4sqrt3x^3+5x-2sqrt3=0`
Find the discriminant of the quadratic equation \[3\sqrt{3} x^2 + 10x + \sqrt{3} = 0\].
The positive value of k for which the equation x2 + kx + 64 = 0 and x2 − 8x + k = 0 will both have real roots, is
Solve the following equation:
(2x+3) (3x-7) = 0
Solve equation using factorisation method:
`5/("x" -2) - 3/("x" + 6) = 4/"x"`
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.
Solve the following equation by factorization
`x^2 - (1 + sqrt(2))x + sqrt(2)` = 0
Two natural numbers are in the ratio 3 : 4. Find the numbers if the difference between their squares is 175.
