The sum of two positive numbers is 90, and the sum of their squares is 4068. Find the smaller number.
Answer and explanation
Correct answer: 42
Let the smaller number be x; then the other number is 90 − x. Thus, \(x^2+(90-x)^2=4068\), which simplifies to \(2x^2-180x+4032=0\), or \(x^2-90x+2016=0\). Factoring gives \((x-42)(x-48)=0\), so the two numbers are 42 and 48. Therefore, the smaller number is 42. Exam tip: When the sum and the sum of squares are given, you can also use \(a^2+b^2=(a+b)^2-2ab\) to find the numbers efficiently.
Frequently asked questions
What is the correct answer to this question?
42
Why is this the correct answer?
Let the smaller number be x; then the other number is 90 − x. Thus, \(x^2+(90-x)^2=4068\), which simplifies to \(2x^2-180x+4032=0\), or \(x^2-90x+2016=0\). Factoring gives \((x-42)(x-48)=0\), so the two numbers are 42 and 48. Therefore, the smaller number is 42. Exam tip: When the sum and the sum of squares are given, you can also use \(a^2+b^2=(a+b)^2-2ab\) to find the numbers efficiently.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Word Problems and Applications.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
