Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2` , x ≠ -1/2, 1
Advertisements
उत्तर
We have been given
`(x-1)/(2x+1)+(2x+1)/(x-1)=5/2`
2(x2 + 1 - 2x + 4x2 + 1 + 4x) = 5(2x2 - x - 1)
10x2 + 4x + 4 = 10x2 - 5x - 5
9x + 9 = 0
Therefore,
9x = -9
x = -9/9
x = -1
Hence, x = -1
APPEARS IN
संबंधित प्रश्न
Solve (i) x2 + 3x – 18 = 0
(ii) (x – 4) (5x + 2) = 0
(iii) 2x2 + ax – a2 = 0; where ‘a’ is a real number
Find the roots of the following quadratic equation by factorisation:
2x2 + x – 6 = 0
The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.
Solve the following quadratic equations by factorization:
`sqrt2x^2-3x-2sqrt2=0`
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
There are three consecutive integers such that the square of the first increased by the product of the first increased by the product of the others the two gives 154. What are the integers?
Solve the following quadratic equations by factorization: \[\frac{x + 1}{x - 1} + \frac{x - 2}{x + 2} = 4 - \frac{2x + 3}{x - 2}; x \neq 1, - 2, 2\]
If one root of the equation 4x2 − 2x + (λ − 4) = 0 be the reciprocal of the other, then λ =
Solve the following equation: 4x2 + 16x = 0
Solve the following equation: `"a"/("x" - "a") + "b"/("x" - "b") = (2"c")/("x" - "c")`
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
The side (in cm) of a triangle containing the right angle are 5x and 3x – 1. If the area of the triangle is 60 cm². Find the sides of the triangle.
Some students planned a picnic. The budget for the food was Rs. 480. As eight of them failed to join the party, the cost of the food for each member increased by Rs. 10. Find how many students went for the picnic.
An aeroplane travelled a distance of 400 km at an average speed of x km/hr. On the return journey the speed was increased by 40 km/hr. Write down the expression for the time taken for
The outward journey
Solve for x:
`(x + 1/x)^2 - (3)/(2)(x - 1/x)-4` = 0.
In each of the following determine whether the given values are solutions of the equation or not.
9x2 - 3x - 2 = 0; x = `-(1)/(3), x = (2)/(3)`
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization
`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
Solve the following equation by factorisation :
`sqrt(3x^2 - 2x - 1) = 2x - 2`
If x = –2 is the common solution of quadratic equations ax2 + x – 3a = 0 and x2 + bx + b = 0, then find the value of a2b.
