Select the correct answerThrice the square of a natural number decreased by 4 times the number is equal to 50 more than the number. The number is ?Options4576

Let's denote the natural number as x.

According to the problem, we have the equation:

3x^2 - 4x = x + 50

Simplifying this, we get:

3x^2 - 5x - 50 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here, a = 3, b = -5, and c = -50.

Substituting these values into the quadratic formula, we get:

x = [5 ± sqrt((-5)^2 - 43(-50))] / (2*3) x = [5 ± sqrt(25 + 600)] / 6 x = [5 ± sqrt(625)] / 6 x = [5 ± 25] / 6

This gives us two possible solutions: x = 30/6 = 5 or x = -20/6 = -10/3.

However, since x is a natural number, it cannot be negative or a fraction. Therefore, the only possible solution is x = 5.

So, the correct answer is 5.

Let's denote the natural number as x.

According to the problem, we have the equation:

3x^2 - 4x = x + 50

Solving this equation, we get:

3x^2 - 4x - x - 50 = 0

This simplifies to:

3x^2 - 5x - 50 = 0

This is a quadratic equation in the form ax^2 + bx + c = 0. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Here, a = 3, b = -5, and c = -50.

Substituting these values into the quadratic formula, we get:

x = [5 ± sqrt((-5)^2 - 43(-50))] / (2*3) x = [5 ± sqrt(25 + 600)] / 6 x = [5 ± sqrt(625)] / 6 x = [5 ± 25] / 6

This gives us two possible solutions: x = 30/6 = 5 and x = -20/6 = -10/3.

However, since x is a natural number, we discard the negative solution.

Therefore, the natural number is 5.