Advertisements
Advertisements
प्रश्न
Find two consecutive positive even integers whose squares have the sum 340.
Advertisements
उत्तर
Let two consecutive positive even integers be 2x, 2x + 2
∴ (2x)2 + (2x + 2)2 = 340
⇒ 4x2 + 4x2 + 4 + 8x = 340
⇒ 8x2 + 8x - 336 = 0
⇒ x2 + x - 42 = 0
⇒ x2 + 7x - 6x - 42 = 0
⇒ x(x + 7) -6(x + 7) = 0
⇒ (x + 7) (x + 6) = 0
⇒ x + 7 = 0 or x - 6 = 0
⇒ x = -7 or x = 6
Negative integer is not required, therefore, x = 6.
Hence, integers are 6 x 2, (6 x 2)+ 2.
i.e., 12 and 14.
संबंधित प्रश्न
Divide 29 into two parts so that the sum of the squares of the parts is 425.
The sum of the squares of two numbers as 233 and one of the numbers as 3 less than twice the other number find the numbers.
A two digits number is such that the product of the digits is 12. When 36 is added to the number, the digits inter change their places determine the number.
A takes 10 days less than the time taken by B to finish a piece of work. If both A and B together can finish the work in 12 days, find the time taken by B to finish the work.
`2x^2+5x-3=0`
Solve the following quadratic equations by factorization:
\[\frac{3}{x + 1} + \frac{4}{x - 1} = \frac{29}{4x - 1}; x \neq 1, -1, \frac{1}{4}\]
The present age of the mother is square of her daughter's present age. 4 years hence, she will be 4 times as old as her daughter. Find their present ages.
Solve equation using factorisation method:
`4/(x + 2) - 1/(x + 3) = 4/(2x + 1)`
Solve the following by reducing them to quadratic form:
`sqrt(x^2 - 16) - (x - 4) = sqrt(x^2 - 5x + 4)`.
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.
