Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`(x-3)/(x+3)-(x+3)/(x-3)=48/7` , x ≠ 3, x ≠ -3
Advertisements
उत्तर
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
संबंधित प्रश्न
Solve for x
:`1/((x-1)(x-2))+1/((x-2)(x-3))=2/3` , x ≠ 1,2,3
Solve the following quadratic equations by factorization:
`(x-a)/(x-b)+(x-b)/(x-a)=a/b+b/a`
The difference of squares of two numbers is 180. The square of the smaller number is 8 times the larger number. Find two numbers.
A pole has to be erected at a point on the boundary of a circular park of diameter 13 meters in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 meters. Is it the possible to do so? If yes, at what distances from the two gates should the pole be erected?
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
Two pipes running together can fill a tank in `11 1/9` minutes. If one pipe takes 5 minutes more than the other to fill the tank separately, find the time in which each pipe would fill the tank separately.
Solve:
(a + b)2x2 – (a + b)x – 6 = 0; a + b ≠ 0
Without solving the following quadratic equation Find the value of p for which the roots are equal
`px^2 - 4x + 3 = 0`
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Solve the following quadratic equation by factorisation.
x2 – 15x + 54 = 0
Solve the following quadratic equations by factorization:
\[16x - \frac{10}{x} = 27\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{7x + 1}{5x - 3} \right) - 4\left( \frac{5x - 3}{7x + 1} \right) = 11; x \neq \frac{3}{5}, - \frac{1}{7}\]
If the equations \[\left( a^2 + b^2 \right) x^2 - 2\left( ac + bd \right)x + c^2 + d^2 = 0\] has equal roots, then
A two digit number is such that the product of the digit is 12. When 36 is added to the number, the digits interchange their places. Find the numbers.
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
In each of the following determine whether the given values are solutions of the equation or not.
x2 + `sqrt(2)` - 4 = 0; x = `sqrt(2)`, x = -2`sqrt(2)`
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.
A rectangular garden 10 m by 16 m is to be surrounded by a concrete walk of uniform width. Given that the area of the walk is 120 square metres, assuming the width of the walk to be x, form an equation in x and solve it to find the value of x.
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
