Advertisements
Advertisements
प्रश्न
Find three successive even natural numbers, the sum of whose squares is 308.
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
The sum of two numbers is 8 and 15 times the sum of their reciprocals is also 8. Find the numbers.
The difference of two natural numbers is 5 and the difference of heir reciprocals is `5/14`Find the numbers
A teacher on attempting to arrange the students for mass drill in the form of solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Find the roots of the quadratic equation \[\sqrt{2} x^2 + 7x + 5\sqrt{2} = 0\].
Solve the following equation: 4x2 + 4 bx - (a2 - b2) = 0
Find two natural numbers which differ by 3 and whose squares have the sum of 117.
The product of a girl's age five years ago and her age 3 years later is 105. Find her present age.
Solve the following equation by factorization
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
A piece of cloth costs Rs. 300. If the piece was 5 metres longer and each metre of cloth costs Rs. 2 less, the cost of the piece would have remained unchanged. How long is the original piece of cloth and what is the rate per metre?
If x4 – 5x2 + 4 = 0; the values of x are ______.
