IDNLearn.com makes it easy to find precise answers to your specific questions. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.
Sagot :
Sure! Let's solve the given equation step-by-step to identify the correct resulting equation.
The given equation is:
[tex]\[ (x - 9)^2 = 81 \][/tex]
To find the solutions for [tex]\( x \)[/tex], we need to take the square root of both sides of the equation. Taking the square root of both sides, we have:
[tex]\[ \sqrt{(x - 9)^2} = \sqrt{81} \][/tex]
The square root of [tex]\( (x - 9)^2 \)[/tex] simplifies to the absolute value of [tex]\( x - 9 \)[/tex], so:
[tex]\[ |x - 9| = 9 \][/tex]
An absolute value equation [tex]\( |A| = B \)[/tex] can be split into two linear equations:
[tex]\[ A = B \quad \text{or} \quad A = -B \][/tex]
Applying this to our equation:
[tex]\[ x - 9 = 9 \quad \text{or} \quad x - 9 = -9 \][/tex]
Therefore, the equation resulting from taking the square root of both sides of [tex]\( (x - 9)^2 = 81 \)[/tex] is:
[tex]\[ x - 9 = \pm9 \][/tex]
So, the correct answer is:
[tex]\[ x - 9 = \pm 9 \][/tex]
The given equation is:
[tex]\[ (x - 9)^2 = 81 \][/tex]
To find the solutions for [tex]\( x \)[/tex], we need to take the square root of both sides of the equation. Taking the square root of both sides, we have:
[tex]\[ \sqrt{(x - 9)^2} = \sqrt{81} \][/tex]
The square root of [tex]\( (x - 9)^2 \)[/tex] simplifies to the absolute value of [tex]\( x - 9 \)[/tex], so:
[tex]\[ |x - 9| = 9 \][/tex]
An absolute value equation [tex]\( |A| = B \)[/tex] can be split into two linear equations:
[tex]\[ A = B \quad \text{or} \quad A = -B \][/tex]
Applying this to our equation:
[tex]\[ x - 9 = 9 \quad \text{or} \quad x - 9 = -9 \][/tex]
Therefore, the equation resulting from taking the square root of both sides of [tex]\( (x - 9)^2 = 81 \)[/tex] is:
[tex]\[ x - 9 = \pm9 \][/tex]
So, the correct answer is:
[tex]\[ x - 9 = \pm 9 \][/tex]
Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for choosing IDNLearn.com. We’re dedicated to providing clear answers, so visit us again for more solutions.