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
In a class test, the sum of Shefali’s marks in Mathematics and English is 30. Had she got 2 marks more in Mathematics and 3 marks less in English, the product of their marks would have been 210. Find her marks in the two subjects
A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solve the following quadratic equations by factorization:
`4(2x – 3)^2 – (2x – 3) – 14 = 0`
Solve the following quadratic equations by factorization: \[\frac{16}{x} - 1 = \frac{15}{x + 1}; x \neq 0, - 1\]
Solve the following quadratic equations by factorization:
\[3\left( \frac{3x - 1}{2x + 3} \right) - 2\left( \frac{2x + 3}{3x - 1} \right) = 5; x \neq \frac{1}{3}, - \frac{3}{2}\]
The perimeter of the right angled triangle is 60cm. Its hypotenuse is 25cm. Find the area of the triangle.
Write the number of zeroes in the end of a number whose prime factorization is 22 × 53 × 32 × 17.
Solve the following equation by factorization
`(x + 1)/(x - 1) + (x - 2)/(x + 2)` = 3
If twice the area of a smaller square is subtracted from the area of a larger square, the result is 14 cm2. However, if twice the area of the larger square is added to three times the area of the smaller square, the result is 203 cm2. Determine the sides of the two squares.
The product of two successive integral multiples of 5 is 300. Then the numbers are:
