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Answer :
To solve the equation [tex]\(c^2 = \frac{144}{169}\)[/tex], we need to find the values of [tex]\(c\)[/tex] that satisfy this equation. Here's a step-by-step guide:
1. Understanding the Equation:
The equation is [tex]\(c^2 = \frac{144}{169}\)[/tex]. This means we are looking for a value of [tex]\(c\)[/tex] such that when it is squared, it equals [tex]\(\frac{144}{169}\)[/tex].
2. Taking the Square Root:
To solve for [tex]\(c\)[/tex], we take the square root of both sides of the equation. This gives us two possible solutions because both the positive and negative values could satisfy the equation when squared.
3. Calculation:
Let's compute the square roots:
- The positive square root of [tex]\(\frac{144}{169}\)[/tex] is [tex]\(\frac{12}{13}\)[/tex].
- The negative square root of [tex]\(\frac{144}{169}\)[/tex] is [tex]\(-\frac{12}{13}\)[/tex].
4. Checking the Options:
- Option (A) [tex]\(c = \frac{12}{13}\)[/tex] is correct.
- Option (B) [tex]\(c = -\frac{12}{13}\)[/tex] is also correct.
- Options (C) [tex]\(c = \frac{14}{15}\)[/tex] and (D) [tex]\(c = -\frac{14}{15}\)[/tex] are not correct as their squared results would not equal [tex]\(\frac{144}{169}\)[/tex].
5. Conclusion:
Thus, the solutions to the equation are [tex]\(c = \frac{12}{13}\)[/tex] and [tex]\(c = -\frac{12}{13}\)[/tex]. Therefore, the correct answers are (A) and (B).
1. Understanding the Equation:
The equation is [tex]\(c^2 = \frac{144}{169}\)[/tex]. This means we are looking for a value of [tex]\(c\)[/tex] such that when it is squared, it equals [tex]\(\frac{144}{169}\)[/tex].
2. Taking the Square Root:
To solve for [tex]\(c\)[/tex], we take the square root of both sides of the equation. This gives us two possible solutions because both the positive and negative values could satisfy the equation when squared.
3. Calculation:
Let's compute the square roots:
- The positive square root of [tex]\(\frac{144}{169}\)[/tex] is [tex]\(\frac{12}{13}\)[/tex].
- The negative square root of [tex]\(\frac{144}{169}\)[/tex] is [tex]\(-\frac{12}{13}\)[/tex].
4. Checking the Options:
- Option (A) [tex]\(c = \frac{12}{13}\)[/tex] is correct.
- Option (B) [tex]\(c = -\frac{12}{13}\)[/tex] is also correct.
- Options (C) [tex]\(c = \frac{14}{15}\)[/tex] and (D) [tex]\(c = -\frac{14}{15}\)[/tex] are not correct as their squared results would not equal [tex]\(\frac{144}{169}\)[/tex].
5. Conclusion:
Thus, the solutions to the equation are [tex]\(c = \frac{12}{13}\)[/tex] and [tex]\(c = -\frac{12}{13}\)[/tex]. Therefore, the correct answers are (A) and (B).
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