Question

3√х=12 x-2y=26 система уравнений

Answer 1

Ответ:

(16; - 5) - решение системы.

Объяснение:

Решить систему уравнений

$\left \{\begin{array}{l} 3\sqrt{x} = 12, \\ x-2y =26. \end{array} \right.$

Так как арифметический квадратный корень определен на множестве неотрицательных чисел, то $x\geq 0.$

$\left \{\begin{array}{l} 3\sqrt{x} = 12, \\ x-2y =26. \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} \sqrt{x} = 12:3, \\ x-2y =26; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} \sqrt{x} = 4, \\ x-2y =26; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x =16, \\ 16-2y =26; \end{array} \right.\Leftrightarrow$

$\Leftrightarrow\left \{\begin{array}{l} x =16, \\ 2y =16-26; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x =16, \\ 2y =-10; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x =16, \\ y =-10:2; \end{array} \right.\Leftrightarrow\left \{\begin{array}{l} x =16, \\ y =-5. \end{array} \right.$

Получили   x=16 ( удовлетворяет условию  $x\geq 0$  ) и y= - 5 .

Тогда (16; - 5) - решение системы .

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Answer 2

To solve the system of equations, we'll first start with the equation 3√x = 12 and then move on to the equation x - 2y = 26.

1. 3√x = 12

To isolate x, we need to get rid of the cube root on the left side. We can do this by cubing both sides of the equation:

(3√x)^3 = 12^3

x = 12^3

x = 1728

Now that we have the value of x, let's move on to the next equation:

2. x - 2y = 26

Now that we know x = 1728, we can substitute this value into the equation:

1728 - 2y = 26

Next, we'll isolate y by moving the constant term to the other side:

-2y = 26 - 1728

-2y = -1702

Finally, divide both sides by -2 to solve for y:

y = -1702 / -2

y = 851

So, the solution to the system of equations is x = 1728 and y = 851.