The square of 11 less than a number is 1156. In the positive case, what is the number?
Answer and explanation
Correct answer: 45
Interpret the statement as the square of 11 less than the number: (x − 11)² = 1156. Since 1156 = 34², taking square roots gives x − 11 = 34 or x − 11 = −34. These produce x = 45 and x = −23 respectively. The phrase “in the positive case” selects x = 45, so option C is correct. A quick check gives (45 − 11)² = 34² = 1156. Option A is the square-root value, not the requested number; options B and D do not make the expression equal to 1156. The sign must not be discarded without considering both roots, but the positivity condition removes the negative solution.
Frequently asked questions
What is the correct answer to this question?
45
Why is this the correct answer?
Interpret the statement as the square of 11 less than the number: (x − 11)² = 1156. Since 1156 = 34², taking square roots gives x − 11 = 34 or x − 11 = −34. These produce x = 45 and x = −23 respectively. The phrase “in the positive case” selects x = 45, so option C is correct. A quick check gives (45 − 11)² = 34² = 1156. Option A is the square-root value, not the requested number; options B and D do not make the expression equal to 1156. The sign must not be discarded without considering both roots, but the positivity condition removes the negative solution.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
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