When 7 is subtracted from a number, the square of the result is 100. In the positive case, what is the original number?
Answer and explanation
Correct answer: 17
The governing concept is solving a square equation while respecting the stated positive case. Let the original number be x. After subtracting 7, the result is x − 7, and its square is 100, so (x − 7)² = 100. Taking square roots gives x − 7 = ±10. Thus x = 17 or x = −3. The phrase “in the positive case” selects the positive original number, x = 17. Substitution verifies it: 17 − 7 = 10 and 10² = 100. Therefore option C is correct. Option A is the square-root value rather than the original number, option B does not satisfy the condition, and option D gives a result whose difference from 7 has square 169.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The governing concept is solving a square equation while respecting the stated positive case. Let the original number be x. After subtracting 7, the result is x − 7, and its square is 100, so (x − 7)² = 100. Taking square roots gives x − 7 = ±10. Thus x = 17 or x = −3. The phrase “in the positive case” selects the positive original number, x = 17. Substitution verifies it: 17 − 7 = 10 and 10² = 100. Therefore option C is correct. Option A is the square-root value rather than the original number, option B does not satisfy the condition, and option D gives a result whose difference from 7 has square 169.
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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