The square of a number is 432 more than 18 times the number. What is the positive number?
Answer and explanation
Correct answer: \(9+3\sqrt{57}\)
Let the number be \(x\). Then \(x^2=18x+432\), so \(x^2-18x-432=0\). Using the quadratic formula, \(x=\frac{18\pm\sqrt{18^2+4\cdot432}}{2}=9\pm3\sqrt{57}\). Since \(9-3\sqrt{57}\) is negative, the positive number is \(9+3\sqrt{57}\). Exam tip: form the quadratic equation first, calculate both roots, and then select the root that satisfies the condition in the question.
Frequently asked questions
What is the correct answer to this question?
\(9+3\sqrt{57}\)
Why is this the correct answer?
Let the number be \(x\). Then \(x^2=18x+432\), so \(x^2-18x-432=0\). Using the quadratic formula, \(x=\frac{18\pm\sqrt{18^2+4\cdot432}}{2}=9\pm3\sqrt{57}\). Since \(9-3\sqrt{57}\) is negative, the positive number is \(9+3\sqrt{57}\). Exam tip: form the quadratic equation first, calculate both roots, and then select the root that satisfies the condition in the question.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
