Questions: x^3 = -5y^2 + 1 at (1,2)

Transcript text: c) $x^{3}=-5 y^{2}+1$ at $(1,2)$

Solution

Solution Steps

To find the value of the given equation $x^3 = -5y^2 + 1$ at the point $(1,2)$, we need to substitute $x = 1$ and $y = 2$ into the equation and solve for the result.

Step 1: Substitute Values

We start with the equation $x^3 = -5y^2 + 1$. We will substitute $x = 1$ and $y = 2$ into the equation.

Step 2: Calculate Each Term

Calculating $x^3$: \[ x^3 = 1^3 = 1 \]

Calculating $-5y^2$: \[ -5y^2 = -5(2^2) = -5 \cdot 4 = -20 \]

Step 3: Combine Results

Now, we combine the results: \[ 1 = -20 + 1 \] This simplifies to: \[ 1 = -19 \]

Step 4: Evaluate the Equation

The left-hand side equals $1$ and the right-hand side equals $-19$. Therefore, the equation does not hold true at the point $(1, 2)$.

Final Answer

The equation $x^3 = -5y^2 + 1$ does not hold at the point $(1, 2)$, so the result is inconsistent. Thus, we conclude: $\boxed{\text{No solution at } (1, 2)}$

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