Advertisements
Advertisements
Question
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
Advertisements
Solution
We have been given
`(x-3)/(x+3)-(x+3)/(x-3)=48/7`
7(x2 + 9 - 6x - x2 - 9 - 6x) = 48(x2 - 9)
48x2 + 84x - 432 = 0
4x2 + 7x - 36 = 0
Therefore,
4x2 + 16x - 9x - 36 = 0
4x(x + 4) - 9(x + 4) = 0
(4x - 9)(x + 4) = 0
Therefore,
4x - 9 = 0
4x = 9
x = 9/4
or,
x + 4 = 0
x = -4
Hence, x = 9/4 or x = -4.
APPEARS IN
RELATED QUESTIONS
Solve the following quadratic equations by factorization:
`2/2^2-5/x+2=0`
The product of Ramu's age (in years) five years ago and his age (in years) nice years later is 15. Determine Ramu's present age.
Some students planned a picnic. The budget for food was Rs. 500. But, 5 of them failed to go and thus the cost of food for each member increased by Rs. 5. How many students attended the picnic?
Solve each of the following equations by factorization:
`x+1/x=2.5`
Solve the following quadratic equation by factorisation.
m2 - 11 = 0
Solve the following quadratic equations by factorization: \[\frac{1}{2a + b + 2x} = \frac{1}{2a} + \frac{1}{b} + \frac{1}{2x}\]
Find the values of k for which the roots are real and equal in each of the following equation:
\[4 x^2 + px + 3 = 0\]
If the equation x2 − ax + 1 = 0 has two distinct roots, then
If x = 1 is a common root of ax2 + ax + 2 = 0 and x2 + x + b = 0, then, ab =
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Five years ago, a woman’s age was the square of her son’s age. Ten years hence, her age will be twice that of her son’s age. Find:
- the age of the son five years ago.
- the present age of the woman.
Solve the following quadratic equation by factorisation method:
`x/(x + 1) + (x + 1)/x = (34)/(15') x ≠ 0, x ≠ -1`
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)`
Solve the following equation by factorization
`(1)/(x + 6) + (1)/(x - 10) = (3)/(x - 4)`
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from both the numerator and denominator, the fraction is decreased by `(1)/(14)`. Find the fraction.
The perimeter of a rectangular plot is 180 m and its area is 1800 m2. Take the length of the plot as x m. Use the perimeter 180 m to write the value of the breadth in terms of x. Use the values of length, breadth and the area to write an equation in x. Solve the equation to calculate the length and breadth of the plot.
At an annual function of a school, each student gives the gift to every other student. If the number of gifts is 1980, find the number of students.
Forty years hence, Mr. Pratap’s age will be the square of what it was 32 years ago. Find his present age.
Solve the following quadratic equation by factorization method.
3p2 + 8p + 5 = 0
Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
