The square of 15 less than a number is 2209. In the positive case, what is the number?
Answer and explanation
Correct answer: 62
Let the number be x. The wording gives (x-15)^2=2209. Since 2209=47^2, taking square roots gives x-15=47 or x-15=-47. The phrase “in the positive case” selects the positive value of x-15, so x-15=47. Therefore x=47+15=62, making option C correct. The other algebraic solution would be x=15-47=-32, which is not the requested positive case. Option A confuses the intermediate value x-15 with x itself; B and D do not satisfy the equation. Substitution verifies the result: (62-15)^2=47^2=2209.
Frequently asked questions
What is the correct answer to this question?
62
Why is this the correct answer?
Let the number be x. The wording gives (x-15)^2=2209. Since 2209=47^2, taking square roots gives x-15=47 or x-15=-47. The phrase “in the positive case” selects the positive value of x-15, so x-15=47. Therefore x=47+15=62, making option C correct. The other algebraic solution would be x=15-47=-32, which is not the requested positive case. Option A confuses the intermediate value x-15 with x itself; B and D do not satisfy the equation. Substitution verifies the result: (62-15)^2=47^2=2209.
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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