Question

Сумма двух чисел равна 15,а произведение 54.найдите эти числа.нужно полностью решение

Answer 1

Эти числа  6 и 9, так как 6*9=54 и 6+9=15.

Answer 2

Solution:

Let's solve the problem step by step.

Let's assume the two numbers are x and y.

We know that the sum of the two numbers is 15, so we can write the equation: x + y = 15.

We also know that the product of the two numbers is 54, so we can write the equation: x * y = 54.

Now, we can use these two equations to solve for the values of x and y.

Solving for the Numbers:

We can use substitution or elimination to solve for the values of x and y. Let's use substitution.

From the equation x + y = 15, we can express y in terms of x as y = 15 - x.

Substituting this value of y into the equation x * y = 54, we get: x * (15 - x) = 54.

Expanding and rearranging the equation, we get a quadratic equation: x^2 - 15x + 54 = 0.

Now, we can solve this quadratic equation to find the values of x and then use those values to find y.

Quadratic Equation Solution:

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a), where a = 1, b = -15, and c = 54.

Plugging in the values, we get: x = (15 ± √(15^2 - 4*1*54)) / (2*1).

Calculating the discriminant and the roots, we get: x = (15 ± √(225 - 216)) / 2, x = (15 ± √9) / 2, x = (15 ± 3) / 2.

So, we have two possible values for x: x = (15 + 3) / 2 = 9 or x = (15 - 3) / 2 = 6.

Finding the Numbers:

Now that we have the values of x, we can find the corresponding values of y using the equation y = 15 - x.

For x = 9, y = 15 - 9 = 6. For x = 6, y = 15 - 6 = 9.

Therefore, the two numbers are 6 and 9.

So, the numbers that satisfy the given conditions are 6 and 9.

Conclusion:

The two numbers that satisfy the given conditions are 6 and 9.