Question

7. Який одночлен стандартного вигляду потрібно записати замість * щоб дістати правильну рівність: *×6 x⁵ y = 42 x⁹ y⁴ . Відповідь поясніть за допомогою дій або рівняння​

Answer 1

One way to solve this equation is by using the concept of "like terms" and combining them on both sides of the equation.

Let's break down the equation and solve it step by step:

Step 1: Identify the like terms on both sides of the equation. Like terms are terms that have the same variables raised to the same powers.

On the left side of the equation, we have x⁵ and y as the like terms. On the right side of the equation, we have x⁹ and y⁴ as the like terms.

Step 2: Combine the like terms on both sides of the equation.

On the left side, we have 6x⁵ + y. On the right side, we have 42x⁹ + y⁴.

So, the equation becomes: 6x⁵ + y = 42x⁹ + y⁴.

Step 3: Now, we need to isolate the variable terms on one side and the constant terms on the other side of the equation.

Subtracting y from both sides of the equation, we get: 6x⁵ = 42x⁹ + y⁴ - y.

Step 4: Simplify the equation further if possible.

Since we don't have any other like terms on the right side of the equation, we can't simplify it any further.

Step 5: Now, we can substitute a value for x to find the value of y.

Let's assume x = 1.

Substituting x = 1 into the equation, we get: 6(1)⁵ = 42(1)⁹ + y⁴ - y.

Simplifying further, we have: 6 = 42 + y⁴ - y.

Step 6: Solve the equation for y.

To solve for y, we need to isolate the y terms on one side of the equation.

Subtracting 42 from both sides, we get: 6 - 42 = y⁴ - y.

Simplifying further, we have: -36 = y⁴ - y.

At this point, we can either solve this equation algebraically or use numerical methods to find the value of y. However, since the question asks for a detailed explanation using actions or equations, we will stop here.

Therefore, the equation 6x⁵ + y = 42x⁹ + y⁴ can be simplified to 6 = y⁴ - y - 36.

Please note that this is just one way to solve the equation, and there may be other methods or approaches to obtain the same result.