Solve: [tex]$\quad \sqrt{-56+4}+2=7$[/tex]
Answer (2)
The equation − 56 + 4 + 2 = 7 has no real solution because it involves the square root of a negative number. After simplifying the equation to − 52 = 5 , we recognize that the square root of a negative number is not a real number, thus the equation has no real solution. Therefore, the answer is D NE .
Explanation
Problem Setup We are given the equation − 56 + 4 + 2 = 7 and asked to solve for the unknown variable.
Simplify Inside Square Root First, simplify the expression inside the square root: − 56 + 4 = − 52 .
Rewrite the Equation Rewrite the equation as − 52 + 2 = 7 .
Isolate Square Root Isolate the square root term: − 52 = 7 − 2 = 5 .
No Real Solution Since the value inside the square root is negative, − 52 is not a real number. Therefore, there is no real solution to the equation.
Examples
Imagine you are trying to determine the length of a side of a square, but end up with a negative value inside the square root when using the area formula. This indicates that the initial conditions or measurements might be incorrect, or that a real-world solution doesn't exist for the given parameters. Understanding when equations have no real solutions is crucial in various fields, such as physics, engineering, and economics, to identify inconsistencies or limitations in models and calculations. This algebraic skill helps in recognizing when a problem's conditions lead to impossible or undefined results.
The equation − 56 + 4 + 2 = 7 simplifies to − 52 = 5 , but since the square root of a negative number is imaginary, there is no real solution to the equation. Therefore, the answer is D NE (Does Not Exist).
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