Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let the total number of swans be x.
Then, the total number of swans are playing on the share of a pond `7/2 sqrtx.`
It is given that
`7/2 sqrtx + 2 = x`
Let x = y2, then `7/2 y+2=y^2`
`(7y+4)/2=y^2`
2y2 = 7y + 4
2y2 - 7y - 4 = 0
2y2 - 8y + y - 4 = 0
2y(y + 4) - 1(y + 4) = 0
(2y - 1)(y + 4) = 0
2y - 1 = 0
2y = 1
y = 1/2
Or
y + 4 = 0
y = -4
Because y = 1/2 is not correct.
Thus, y = -4 is correct. Putting the value of y
y = -4
`sqrtx= -4`
Square root both sides and we get
`(sqrtx)^2=(-4)^2`
x = 16
Therefore, the total number of swans is x = 16.
APPEARS IN
संबंधित प्रश्न
Solve for x
`(2x)/(x-3)+1/(2x+3)+(3x+9)/((x-3)(2x+3)) = 0, x!=3,`
A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.
Solve the following quadratic equations by factorization:
25x(x + 1) = -4
Solve the following quadratic equations by factorization:
`1/(x-2)+2/(x-1)=6/x` , x ≠ 0
The sum of two numbers is 48 and their product is 432. Find the numbers?
The sum of ages of a man and his son is 45 years. Five years ago, the product of their ages was four times the man's age at the time. Find their present ages.
Solve x2 – 4x – 12 =0; when x ∈ I
Solve:
`1/p + 1/q + 1/x = 1/(x + p + q)`
Solve:
`1/(x + 1) - 2/(x + 2) = 3/(x + 3) - 4/(x + 4)`
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
`x^2-4x+1=0`
Find the two consecutive positive even integers whose product is 288.
Solve the following quadratic equation by factorization.
`2"x"^2 - 2"x" + 1/2 = 0`
If \[x^2 + k\left( 4x + k - 1 \right) + 2 = 0\] has equal roots, then k =
Solve the following equation: a2b2x2 + b2x - a2x - 1 = 0
Two natural numbers differ by 4. If the sum of their square is 656, find the numbers.
Solve the following quadratic equation using factorization method:
`"x"^2-11"x"+24=0`
A car covers a distance of 400 km at a certain speed. Had the speed been 12 km/hr more, the time taken for the journey would have been 1 hour 40 minutes less. Find the original speed of the car.
The hypotenuse of a right-angled triangle is 1 m less than twice the shortest side. If the third side is 1 m more than the shortest side, find the sides of the triangle.
Complete the following activity to solve the given quadratic equation by factorization method.
Activity: x2 + 8x – 20 = 0
x2 + ( __ ) – 2x – 20 = 0
x (x + 10) – ( __ ) (x + 10) = 0
(x + 10) ( ____ ) = 0
x = ___ or x = 2
