Question

If 10 is added to two-third of the square of a natural number the sum is 34 find the number​

Answer 1

Explanation:

Let's assume the natural number is "x."

According to the given information, we can write the equation as:

2/3 * x² + 10 = 34

First, subtract 10 from both sides:

2/3 * x² = 24

Next, multiply both sides by 3:

2 * x² = 72

2x² = 72

Divide both sides by 2:

x² = 36

Now, take the square root of both sides:

x = √36

x = 6 or x = -6

Since we are dealing with a natural number, the only valid solution is x = 6.

Therefore, the number is 6.

Answer 2

number is 6

Explanation:

let n be the natural number then the square is n² and two- thirds of this is

`(2)/(3)` n² ( add 10 and equate the result to 34 )

`(2)/(3)` n² + 10 = 34 ( subtract 10 from both sides )

`(2)/(3)` n² + 10 - 10 = 34 - 10 ( simplify )

`(2)/(3)` n² = 24 ( multiply both sides by 3 to clear the fraction )

3 ×
`(2)/(3)` n² = 3 × 24 ( simplify )

2n² = 72 ( divide both sides by 2 )

n² = 36 ( take square root of both sides )

`√(n^2)` = ±
`√(36)` , that is

n = ± 6

- 6 is an integer not a natural number and 6 is a natural number

thus the number is 6