Advertisements
Advertisements
प्रश्न
Solve the following quadratic equations by factorization:
`(x+1)/(x-1)-(x-1)/(x+1)=5/6` , x ≠ 1, x ≠ -1
Advertisements
उत्तर
We have been given
`(x+1)/(x-1)-(x-1)/(x+1)=5/6`
6(x2 + 1 + 2x - x2 - 1 + 2x) = 5(x2 - 1)
5x2 - 24x - 5 = 0
5x2 - 25x + x - 5 = 0
5x(x - 5) + 1(x - 5) = 0
(5x + 1)(x - 5) = 0
Therefore,
5x + 1 = 0
5x = -1
x = -1/5
Or,
x - 5 = 0
x = 5
Hence, x = -1/5 or x = 5
APPEARS IN
संबंधित प्रश्न
Solve for x :
`2/(x+1)+3/(2(x-2))=23/(5x), x!=0,-1,2`
Solve the following quadratic equations by factorization:
`x^2+(a+1/a)x+1=0`
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
An aeroplane take 1 hour less for a journey of 1200 km if its speed is increased by 100 km/hr from its usual speed. Find its usual speed.
Solve the following quadratic equations by factorization:
`(x + 3)^2 – 4(x + 3) – 5 = 0 `
The sum of a natural number and its square is 156. Find the number.
A quadratic equation whose one root is 2 and the sum of whose roots is zero, is ______.
Solve the following equation: `("a+b")^2 "x"^2 - 4 "abx" - ("a - b")^2 = 0`
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve equation using factorisation method:
`2x^2 - 1/2x = 0`
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 return Journey. If the return journey took 30 minutes less than the onward journey write down an equation in x and find its value.
In each of the following, determine whether the given values are solution of the given equation or not:
x2 + x + 1 = 0; x = 0; x = 1
Solve the following equation by factorization
21x2 – 8x – 4 = 0
Solve the following equation by factorization
3x2= x + 4
Solve the following equation by factorization
2x2 – 9x + 10 = 0,when x∈Q
Solve the following equation by factorization.
a2x2 + 2ax + 1 = 0, a ≠ 0
Solve the following equation by factorization
a2x2 + (a2+ b2)x + b2 = 0, a ≠ 0
Use the substitution y = 3x + 1 to solve for x : 5(3x + 1 )2 + 6(3x + 1) – 8 = 0
For equation `1/x + 1/(x - 5) = 3/10`; one value of x is ______.
