Advertisements
Advertisements
प्रश्न
The ratio of two numbers is 3:2 and the difference of their square is 500. Find the numbers.
उत्तर
Given: Ratio of two numbers = 3:2
So, let the two numbers be 3x and 2x.
Now, according to the question,
(3x)2 – (2x)2 = 500
⇒ 9x2 – 4x2 = 500
⇒ 5x2 = 500
⇒ x2 = `500/5` = 100
⇒ x = `sqrt(100)`
⇒ x = ± 10
For x = – 10,
First number = 3 × (– 10) = – 30
and second number = 2 × (–10) = – 20
For x = 10,
First number = 3 × (10) = 30
and second number = 2 × (10) = 20
Hence, the numbers are – 30, – 20 or 30, 20.
APPEARS IN
संबंधित प्रश्न
Solve the following quadratic equation for x: `4x^2 + 4bx – (a^2 – b^2) = 0`
Sum of the areas of two squares is 468 m2. If the difference of their perimeters is 24 m, find the sides of the two squares.
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
`x^2-4sqrt2x+6=0`
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
`sqrt2x^2-3x-2sqrt2=0`
Find the roots of the following quadratic equations (if they exist) by the method of completing the square.
`x^2-(sqrt2+1)x+sqrt2=0`
The length of a rectangle is thrice as long as the side of a square. The side of the square is 4 cm more than the width of the rectangle. Their areas being equal, find the dimensions.
The hypotenuse of a right-angled triangle is 1 meter less than twice the shortest side. If the third side 1 meter more than the shortest side, find the side, find the sides of the triangle.
Solve the following quadratic equation by completing the square method.
2y2 + 9y + 10 = 0
Form the quadratic equation from the roots given below.
0 and 4
Form the quadratic equation from the roots given below.
\[2 - \sqrt{5}, 2 + \sqrt{5}\]
α, β are roots of y2 – 2y –7 = 0 find,
α2 + β2
α, β are roots of y2 – 2y –7 = 0 find,
α3 + β3
The difference of two natural numbers is 3 and the difference of their reciprocals is \[\frac{3}{28}\].Find the numbers.
In a flight of 600 km, an aircraft was slowed due to bad weather. Its average speed for the trip was reduced by 200 km/hr and the time of the flight increased by 30 minutes. Find the scheduled duration of the flight.
Solve the following quadratic equation by completing square: z2 + 4z - 7 = 0.
For solving the quadratic equations `"x"^2 + 8"x" =-15` by completing the square method, find the third term.
A chess board contains 64 equal squares and the area of each square is 6.25 cm2. A border round the board is 2 cm wide. The length of the side of the chess board is:
The sum of the squares of two consecutive natural numbers is 313. The numbers are:
Find the value of x, if `(4/7)^x (7/4)^(2x) = 343/64`.
