What are the values of \(x\) when the equation \(x^2=121\) is solved by the square root method?
Answer and explanation
Correct answer: \(x=\pm 11\)
Taking square roots gives \(x=\pm\sqrt{121}=\pm 11\), so both \(x=11\) and \(x=-11\) are solutions. Writing only \(x=11\) is incomplete because \((-11)^2\) is also 121; \(\pm121\) results from not taking the square root. Exam tip: for \(x^2=a\) with \(a>0\), always write both roots as \(x=\pm\sqrt{a}\).
Frequently asked questions
What is the correct answer to this question?
\(x=\pm 11\)
Why is this the correct answer?
Taking square roots gives \(x=\pm\sqrt{121}=\pm 11\), so both \(x=11\) and \(x=-11\) are solutions. Writing only \(x=11\) is incomplete because \((-11)^2\) is also 121; \(\pm121\) results from not taking the square root. Exam tip: for \(x^2=a\) with \(a>0\), always write both roots as \(x=\pm\sqrt{a}\).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Quadratic Equations. Topic: Methods of Solving Quadratic Equations.
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