Question

Найдите корень уравнения, выраженный натуральным числом: 1) X (X+10)=119 2) X(X-18)=115 3) X (X+2)=143

Answer 1

Через дискриминант решай и скобки сначала раскрой. D=b^2-4ac
x=-b+-корень из D/2 (2-это знаменатель дроби)

Answer 2

1) X(X + 10) = 119

To find the root of this equation, we need to solve for X. Let's simplify the equation first by expanding the brackets:

X^2 + 10X = 119

Now, we have a quadratic equation. To solve it, we can either factorize or use the quadratic formula. In this case, let's use the quadratic formula:

The quadratic formula states that for an equation in the form Ax^2 + Bx + C = 0, the solutions for x are given by:

x = (-B ± √(B^2 - 4AC)) / (2A)

In our equation, A = 1, B = 10, and C = -119. Substituting these values into the quadratic formula, we get:

x = (-10 ± √(10^2 - 4(1)(-119))) / (2(1))

Simplifying further:

x = (-10 ± √(100 + 476)) / 2 x = (-10 ± √576) / 2 x = (-10 ± 24) / 2

Now we have two possible solutions:

x1 = (-10 + 24) / 2 = 14 / 2 = 7 x2 = (-10 - 24) / 2 = -34 / 2 = -17

However, we are looking for a natural number solution, which means x must be a positive integer. Therefore, the only valid solution is x = 7.

2) X(X - 18) = 115

Let's simplify the equation by expanding the brackets:

X^2 - 18X = 115

Again, we have a quadratic equation. Using the quadratic formula:

x = (-B ± √(B^2 - 4AC)) / (2A)

In our equation, A = 1, B = -18, and C = -115. Substituting these values into the quadratic formula, we get:

x = (-(-18) ± √((-18)^2 - 4(1)(-115))) / (2(1)) x = (18 ± √(324 + 460)) / 2 x = (18 ± √784) / 2 x = (18 ± 28) / 2

Now we have two possible solutions:

x1 = (18 + 28) / 2 = 46 / 2 = 23 x2 = (18 - 28) / 2 = -10 / 2 = -5

Since we are looking for a natural number solution, the only valid solution is x = 23.

3) X(X + 2) = 143

Let's simplify the equation by expanding the brackets:

X^2 + 2X = 143

Again, we have a quadratic equation. Using the quadratic formula:

x = (-B ± √(B^2 - 4AC)) / (2A)

In our equation, A = 1, B = 2, and C = -143. Substituting these values into the quadratic formula, we get:

x = (-2 ± √(2^2 - 4(1)(-143))) / (2(1)) x = (-2 ± √(4 + 572)) / 2 x = (-2 ± √576) / 2 x = (-2 ± 24) / 2

Now we have two possible solutions:

x1 = (-2 + 24) / 2 = 22 / 2 = 11 x2 = (-2 - 24) / 2 = -26 / 2 = -13

Since we are looking for a natural number solution, the only valid solution is x = 11.

In summary, the roots expressed as natural numbers for the given equations are: 1) x = 7 2) x = 23 3) x = 11