Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
Advertisements
उत्तर
\[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}\]
\[ \Rightarrow \frac{3\left( x - 1 \right) + 4\left( x + 1 \right)}{\left( x + 1 \right)\left( x - 1 \right)} = \frac{29}{4x - 1}\]
\[ \Rightarrow \frac{3x - 3 + 4x + 4}{x^2 - 1} = \frac{29}{4x - 1}\]
\[ \Rightarrow \frac{7x + 1}{x^2 - 1} = \frac{29}{4x - 1}\]
\[ \Rightarrow \left( 7x + 1 \right)\left( 4x - 1 \right) = 29\left( x^2 - 1 \right)\]
\[ \Rightarrow 28 x^2 - 7x + 4x - 1 = 29 x^2 - 29\]
\[ \Rightarrow 29 x^2 - 28 x^2 + 3x - 28 = 0\]
\[ \Rightarrow x^2 + 3x - 28 = 0\]
\[ \Rightarrow x^2 + 7x - 4x - 28 = 0\]
\[ \Rightarrow x(x + 7) - 4(x + 7) = 0\]
\[ \Rightarrow (x - 4)(x + 7) = 0\]
\[ \Rightarrow x - 4 = 0 \text { or } x + 7 = 0\]
\[ \Rightarrow x = 4 \text { or } x = - 7\]
Hence, the factors are 4 and −7.
APPEARS IN
संबंधित प्रश्न
The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and original fraction is `29/20`. Find the original fraction.
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
Solve the following quadratic equation by factorization:
`(x-5)(x-6)=25/(24)^2`
A passenger train takes 3 hours less for a journey of 360 km, if its speed is increased by 10 km/hr from its usual speed. What is the usual speed?
A plane left 40 minutes late due to bad weather and in order to reach its destination, 1600 km away in time, it had to increase its speed by 400 km/hr from its usual speed. Find the usual speed of the plane.
An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.
Out of a group of swans, 7/2 times the square root of the total number are playing on the share of a pond. The two remaining ones are swinging in water. Find the total number of swans.
For the equation given below, find the value of ‘m’ so that the equation has equal roots. Also, find the solution of the equation:
x2 – (m + 2)x + (m + 5) = 0
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} - \frac{1}{2} = \frac{2}{3x - 1}, x \neq - 1, \frac{1}{3}\]
Solve the following quadratic equations by factorization: \[\sqrt{3} x^2 - 2\sqrt{2}x - 2\sqrt{3} = 0\]
Solve the following equation: `"x"^2 - ( sqrt 2 + 1) "x" + sqrt 2 = 0 `
Solve the following equation: `"a"("x"^2 + 1) - x("a"^2 + 1) = 0`
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Find two consecutive natural numbers whose squares have the sum 221.
Solve the following by reducing them to quadratic form:
`sqrt(y + 1) + sqrt(2y - 5) = 3, y ∈ "R".`
Solve the following equation by factorization
2x2 – 8x – 24 = 0 when x∈I
Solve the following equation by factorization
`(8)/(x + 3) - (3)/(2 - x)` = 2
Solve the following equation by factorization
`(1)/(2a + b + 2x) = (1)/(2a) + (1)/b + (1)/(2x)`
Five times a certain whole number is equal to three less than twice the square of the number. Find the number.
The lengths of the parallel sides of a trapezium are (x + 9) cm and (2x – 3) cm and the distance between them is (x + 4) cm. If its area is 540 cm2, find x.
