A positive number when decreased by 4 is equal to 21 times the reciprocal of the number. Find the number?Options191287

Let's denote the number as x.

According to the problem, we have the equation:

x - 4 = 21 * (1/x)

To solve this equation, we can first multiply each side by x to get rid of the fraction:

x^2 - 4x = 21

Then, we rearrange the equation to a standard quadratic form:

x^2 - 4x - 21 = 0

This is a quadratic equation, and we can solve it by factoring:

(x - 7)(x + 3) = 0

Setting each factor equal to zero gives the solutions x = 7 and x = -3.

However, the problem specifies that x is a positive number, so x = -3 is not a valid solution.

Therefore, the number we are looking for is 7.

Let's denote the number as x.

According to the problem, we have the equation:

x - 4 = 21 * (1/x)

To solve this equation, we can first multiply each side by x to get rid of the fraction:

x^2 - 4x = 21

Then, we rearrange the equation to form a quadratic equation:

x^2 - 4x - 21 = 0

We can factor this equation:

(x - 7)(x + 3) = 0

Setting each factor equal to zero gives the solutions x = 7 and x = -3.

However, the problem specifies that the number is positive, so the number we are looking for is 7.

Let's denote the number as x.

According to the problem, we have the equation:

x - 4 = 21 * (1/x)

To solve this equation, we can first multiply each side by x to get rid of the fraction:

x^2 - 4x = 21

Then, we rearrange the equation to a standard quadratic form:

x^2 - 4x - 21 = 0

This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -4, and c = -21.

We can solve this equation using the quadratic formula: x = [-b ± sqrt(b^2 - 4ac)] / (2a)

Substituting the values of a, b, and c into the formula, we get:

x = [4 ± sqrt((-4)^2 - 41(-21))] / (2*1) x = [4 ± sqrt(16 + 84)] / 2 x = [4 ± sqrt(100)] / 2 x = [4 ± 10] / 2

So, the solutions are x = 7 and x = -3.

However, the problem states that the number is positive, so the number we are looking for is 7.

Therefore, the correct option is 7.