Use ChaGPT to answer math questions from the Matric National Senior Certificate, Grade 12 June 2022 Mathematics P1 paper..

**USER:**

Solve for x:

x^{²=-4x}

**ChatGPT:**

We can start by rearranging the equation and getting zero on one side:

x² + 4x = 0

Now we can factor out x:

x(x + 4) = 0

Using the zero product property, we can conclude that:

x = 0 or x + 4 = 0

Therefore, the solutions are:

x = 0 or x = -4

**USER:**

Solve for x and y simultaneously:

6x+4y²=3-5xy

**ChatGPT:**

To solve for x and y simultaneously, we need to find two equations that we can use to eliminate one variable and solve for the other. One way to do this is to use the two given equations to eliminate one of the variables, and then solve for the other variable.

We can start by rearranging the given equation to get it in the standard form:

5xy + 6x + 4y² – 3 = 0

Next, we can use the quadratic formula to solve for y² in terms of x:

y² = (-6x ± √((6x)² – 4(5)(-3 – 5xy))) / 8

y² = (-6x ± √(36x² + 80xy + 60)) / 8

y² = (-3x ± √(9x² + 20xy + 15)) / 4

Now we can substitute this expression for y² into the original equation, and simplify:

6x + 4((-3x ± √(9x² + 20xy + 15)) / 4)² = 3 – 5x((-3x ± √(9x² + 20xy + 15)) / 4)

Simplifying further, we get:

6x + 9x² + 4(9x² + 20xy + 15) / 16 = 3 + 15x² – 5x(± 3x ± √(9x² + 20xy + 15)) / 4

Multiplying both sides by 16 to eliminate the fractions, and simplifying, we get:

84x² + 80xy + 39 = 0

Now we have two equations:

5xy + 6x + 4y² – 3 = 0

84x² + 80xy + 39 = 0

We can use the second equation to solve for y in terms of x, and then substitute into the first equation to solve for x:

y = (-84x² – 39) / (80x)

Substituting into the first equation, we get:

5x(-84x² – 39) / (80x) + 6x + 4((-84x² – 39) / (80x))² – 3 = 0

Multiplying both sides by 320x to eliminate the fractions, and simplifying, we get:

-336x³ – 143x² – 720x + 900 = 0

We can use numerical methods to approximate the solutions for x, such as the Newton-Raphson method or the bisection method. However, there is no algebraic solution to this equation.