What are the solutions of the equation \(x^2-81=0\)?
Answer and explanation
Correct answer: \(x=\pm 9\)
From \(x^2-81=0\), we get \(x^2=81=9^2\). Hence, \(x=9\) or \(x=-9\), which is written as \(x=\pm9\). Options C and D give only one of the two valid roots, while option B incorrectly treats 81 as the square root of 81. Exam tip: use the difference of squares, \(a^2-b^2=(a-b)(a+b)\), to find both roots quickly.
Frequently asked questions
What is the correct answer to this question?
\(x=\pm 9\)
Why is this the correct answer?
From \(x^2-81=0\), we get \(x^2=81=9^2\). Hence, \(x=9\) or \(x=-9\), which is written as \(x=\pm9\). Options C and D give only one of the two valid roots, while option B incorrectly treats 81 as the square root of 81. Exam tip: use the difference of squares, \(a^2-b^2=(a-b)(a+b)\), to find both roots quickly.
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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