Natural Number Problems and Equations

The video tutorial covers solving various quadratic equations involving natural numbers, even numbers, and consecutive integers. It includes problems on the sum of squares, division into parts, and differences in cubes. The tutorial demonstrates forming equations based on given conditions and solving them to find the required numbers.

What is the sum of the squares of two consecutive natural numbers if the first number is 7?

• 113

• 100

• 85

• 50

If x is a natural number, what is the solution to the equation x² + x - 56 = 0?

• x = 7

• x = 8

• x = -7

• x = -8

What are the two consecutive even natural numbers whose squares sum up to 100?

• 6 and 8

• 4 and 6

• 8 and 10

• 10 and 12

A natural number is greater than twice its square root by 3. What is the number?

• 9

• 36

• 16

• 25

If the sum of the first n natural numbers is 276, what is the value of n?

• 23

• 24

• 26

• 25

The sum of a natural number and its reciprocal is 10/3. What is the natural number?

• 3

• 4

• 5

• 6

Divide 40 into two parts such that the sum of their reciprocals is 8/75. What are the parts?

• 30 and 10

• 20 and 20

• 35 and 5

• 25 and 15

A natural number is greater than three times its square root by 4. What is the number?

• 16

• 9

• 25

• 36

What is the largest number in the product of four consecutive positive integers that equals 840?

• 10

• 9

• 8

• 7

Find the five consecutive natural numbers whose squares sum up to 1455.

• 25, 26, 27, 28, 29

• 15, 16, 17, 18, 19

• 20, 21, 22, 23, 24

• 10, 11, 12, 13, 14