Advertisements
Advertisements
प्रश्न
Find three successive even natural numbers, the sum of whose squares is 308.
Advertisements
उत्तर
Let first even number = 2x
second even number = 2x + 2
third even number = 2x + 4
Now according to the condition,
(2x)2 + (2x + 2)2 + (2x + 4)2 = 308
⇒ 4x2 + 4x2 + 8x + 4 + 4x2 + 16x + 16 = 308
⇒ 12x2 + 24x + 20 - 308 = 0
⇒ 12x2 + 24x - 288 = 0
⇒ x2 + 2x - 24 = 0 ...(Dividing y 12)
⇒ x2 + 6x - 4x - 24 = 0
⇒ x(x + 6) -4(x + 6) = 0
⇒ (x + 6)(x - 4) = 0
Either x + 6 = 0,
then x = -6
But i is not a natural number, hence not possible.
or
x - 4 = 0,
then x = 4
∴ First even natural number = 2x = 2 x 4 = 8
second number = 8 + 2 = 10
and the third number = 10 + 2 = 12.
APPEARS IN
संबंधित प्रश्न
If the list price of a toy is reduced by Rs. 2, a person can buy 2 toys more for Rs. 360. Find the original price of the toy.
The difference of two natural number is 3 and the difference of their reciprocals is `3/28`Find the numbers.
Solve the following quadratic equations by factorization: \[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, - 1, \frac{1}{4}\]
If sin α and cos α are the roots of the equations ax2 + bx + c = 0, then b2 =
Solve the following equation: c
Solve the following equation:
`("x" + 1)/("x" - 1) - ("x" - 1)/("x" + 1) = 5/6 , "x" ≠ -1,1`
The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 124. Determine their present ages.
A rectangle of area 105 cm² has its length equal to x cm. Write down its breadth in terms of x. Given that the perimeter is 44 cm, write down an equation in x and solve it to determine the dimensions of the rectangle.
An aeroplane flying with a wind of 30 km/hr takes 40 minutes less to fly 3600 km, than what it would have taken to fly against the same wind. Find the planes speed of flying in still air.
The product of two integers is –18; the integers are ______.
