Advertisements
Advertisements
Question
Out of a group of Swans, 3 and half times the square root of the total number are playing on the shore of a pond. The two remaining ones are swinging in water. Find the total number of swans.
Solution
Let the total number of swans be a.
Then, 3.5x -`sqrt "a"` + 2 = a
⇒ 3.5x -`sqrt "a"` = a - 2
Squaring both sides, we get:
12.25 a = a2 + 4 - 4a
⇒ a2 -16.2 5a + 4 = 0
⇒ (a-16 ) (a - 0.25) = 0
Hence, total number of swans = 16
APPEARS IN
RELATED QUESTIONS
Find the value of a, b, c in the following quadratic equation : 2x2 ‒ x ‒ 3 = 0
Verify whether 1 is the root of the quadratic equation : `x^2+3x-4=0`
If the equation (1 + m2) x2 + 2mcx + c2 – a2 = 0 has equal roots then show that c2 = a2 (1 + m2)
If quadratic equation x2 – (m + 1) x + 6=0 has one root as x =3; find the value of m and the root of the equation
Solve `a^2x^2 - b^2 = 0`
If x = − 3 and` x = 2/3 `are solution of quadratic equation `mx^2 + 7x + n = 0`, find the values of m and n.
The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.
Find the values of m for which equation 3x2 + mx + 2 = 0 has equal roots. Also, find the roots of the given equation.
In each of the following, determine whether the given numbers are solutions of the given equation or not: `x^2 - 3sqrt(3)x + 6 = 0; sqrt(3), -2sqrt(3)`
Solve the following equation by using formula :
2x2 – 7x + 6 = 0
