In a two-digit number, the units digit is 1 more than the tens digit. The sum of the squares of the two digits is 61. What is the number?
Answer and explanation
Correct answer: 56
Let the tens digit be \(x\). Then the units digit is \(x+1\). Therefore, \(x^2+(x+1)^2=61\), which gives \(2x^2+2x-60=0\) or \(x^2+x-30=0\). Thus, \((x-5)(x+6)=0\), so \(x=5\) or \(x=-6\). Since a digit cannot be negative, the tens digit is 5 and the units digit is 6; hence the number is 56. Exam tip: In digit problems, reject roots that are negative or greater than 9. The nearby option 67 has consecutive digits, but their squared sum is 36+49=85, not 61.
Frequently asked questions
What is the correct answer to this question?
56
Why is this the correct answer?
Let the tens digit be \(x\). Then the units digit is \(x+1\). Therefore, \(x^2+(x+1)^2=61\), which gives \(2x^2+2x-60=0\) or \(x^2+x-30=0\). Thus, \((x-5)(x+6)=0\), so \(x=5\) or \(x=-6\). Since a digit cannot be negative, the tens digit is 5 and the units digit is 6; hence the number is 56. Exam tip: In digit problems, reject roots that are negative or greater than 9. The nearby option 67 has consecutive digits, but their squared sum is 36+49=85, not 61.
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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