Question

Б) xy + 20 = 5x + 4y;B) x √y - 3 = x - 3√y.​

Answer 1

Ответ:

б) x = 4, y = 5

в) x = -3, x√y = 3√y = x + 3

Answer 2

To solve the given equations, let's start with each one separately:

A) xy + 20 = 5x + 4y

To solve this equation, we need to rearrange it into a standard quadratic form. To do that, let's move all the terms containing 'x' to one side of the equation and the terms containing 'y' to the other side:

xy - 5x - 4y = -20

Now, we can factor out 'x' from the terms involving 'x' and 'y' from the terms involving 'y':

x(y - 5) - 4(y - 5) = -20

Now, factor out the common term (y - 5):

(x - 4)(y - 5) = -20

Now, we have the equation in factored form. To solve for 'x' and 'y', we need more information about the relationship between 'x' and 'y'. If you have additional equations or constraints, please provide them, and I can help you solve the system of equations.

B) x√y - 3 = x - 3√y

To solve this equation, let's try to isolate the square root term and the square root with 'y' terms on one side of the equation:

x√y + 3√y = x + 3

Now, factor out the common term (√y):

√y(x + 3) = x + 3

Next, divide both sides by (x + 3):

√y = (x + 3)/(x + 3)

Now, we have:

√y = 1

To solve for 'y,' square both sides:

y = (1)^2

y = 1

Now that we have the value of 'y,' we can substitute it back into either of the original equations to solve for 'x.' Let's use the first equation:

x√y - 3 = x - 3√y

Substitute y = 1:

x√1 - 3 = x - 3√1

Simplify:

x - 3 = x - 3

Now, it appears that this equation is an identity. This means that for any value of 'x,' the equation will always hold true. As a result, there are infinitely many solutions for 'x' that satisfy this equation.

In conclusion:

A) The equation (x - 4)(y - 5) = -20 requires additional information or constraints to solve for 'x' and 'y.'

B) The equation has infinitely many solutions for 'x' when 'y = 1.'