The sum of a number and its square is 1892. What is the positive number?
Answer and explanation
Correct answer: 43
Let the number be \(x\). Then \(x^2+x=1892\), so \(x^2+x-1892=0\). Factoring gives \((x-43)(x+44)=0\), hence \(x=43\) or \(x=-44\). Therefore, the positive number is \(43\). Verification: \(43^2+43=1849+43=1892\); 42 and 44 do not produce this sum. Exam tip: Check the signs of both roots and select only the positive root when the question specifies it.
Frequently asked questions
What is the correct answer to this question?
43
Why is this the correct answer?
Let the number be \(x\). Then \(x^2+x=1892\), so \(x^2+x-1892=0\). Factoring gives \((x-43)(x+44)=0\), hence \(x=43\) or \(x=-44\). Therefore, the positive number is \(43\). Verification: \(43^2+43=1849+43=1892\); 42 and 44 do not produce this sum. Exam tip: Check the signs of both roots and select only the positive root when the question specifies it.
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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