Question

solve ( y^2 = -64 ), where ( y ) is a real number. simplify your answer as much as possible. if there is more than one solution, separate them with commas. if there is no solution, click on
o solution\. ( y = square )

Explanation:

Step1: Analyze the equation

We have the equation \( y^{2}=-64 \), and we are looking for real - number solutions. For any real number \( y \), the square of a real number \( y^{2}\geq0 \) because if \( y \) is positive, \( y^{2}=y\times y>0 \); if \( y = 0 \), \( y^{2}=0 \); if \( y \) is negative, \( y^{2}=(-y)\times(-y)>0 \) (since the product of two negative numbers is positive).

Step2: Compare with the right - hand side

The right - hand side of the equation is \(-64\), which is a negative number. Since the square of any real number is non - negative and \(-64<0\), there is no real number \( y \) that satisfies the equation \( y^{2}=-64 \).

Answer:

No solution