Advertisements
Advertisements
Question
Solve the following equation by factorization
`3x - (8)/x `= 2
Advertisements
Solution
`3x - (8)/x `= 2
`(3x^2 - 8)/x` = 2
⇒ 3x2 - 8 = 2x
⇒ 3x2 - 2x - 8 = 0
⇒ 3x2 - 6x + 4x - 8 = 0
⇒ 3x(x - 2) + 4(x - 2) = 0
⇒ (x - 2)(3x + 4) = 0
Either x - 2 = 0,
then x = 2
or
3x + 4 = 0,
then 3x = -4
⇒ x = `(-4)/(3)`
Hence x = 2, `(-4)/(3)`.
APPEARS IN
RELATED QUESTIONS
A piece of cloth costs Rs. 35. If the piece were 4 m longer and each meter costs Rs. 1 less, the cost would remain unchanged. How long is the piece?
Solve the following quadratic equation by factorisation.
m2 - 11 = 0
If 2 is a root of the quadratic equation \[3 x^2 + px - 8 = 0\] and the quadratic equation \[4 x^2 - 2px + k = 0\] has equal roots, find the value of k.
Show that x = –2 is a solution of 3x2 + 13x + 14 = 0.
The hypotenuse of a right-angled triangle is 17cm. If the smaller side is multiplied by 5 and the larger side is doubled, the new hypotenuse will be 50 cm. Find the length of each side of the triangle.
Solve equation using factorisation method:
x2 – (a + b)x + ab = 0
In a two digit number, the unit’s digit is twice the ten’s digit. If 27 is added to the number, the digit interchange their places. Find the number.
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:
`x^2 - sqrt(2) - 4 = 0; x = -sqrt(2), x = -2sqrt(2)`
A man spent Rs. 2800 on buying a number of plants priced at Rs x each. Because of the number involved, the supplier reduced the price of each plant by Rupee 1.The man finally paid Rs. 2730 and received 10 more plants. Find x.
