The square of a positive number is 22 more than nine times the number. What is the number?
Answer and explanation
Correct answer: 11
Let the number be \(x\). Then \(x^2=9x+22\), so \(x^2-9x-22=0\). Factoring gives \((x-11)(x+2)=0\), hence \(x=11\) or \(x=-2\). Since the number is positive, \(-2\) is rejected, making 11 the correct answer. Exam tip: Translate the wording into an equation first, then apply the condition that the required number must be positive.
Frequently asked questions
What is the correct answer to this question?
11
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=9x+22\), so \(x^2-9x-22=0\). Factoring gives \((x-11)(x+2)=0\), hence \(x=11\) or \(x=-2\). Since the number is positive, \(-2\) is rejected, making 11 the correct answer. Exam tip: Translate the wording into an equation first, then apply the condition that the required number must be positive.
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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