Which of the following is the value of \,((\sqrt{11}+2)(\sqrt{11}-2))\,?
Answer and explanation
Correct answer: 7
This is a product of conjugates; use the identity \((a+b)(a-b)=a^2-b^2\). With \(a=\sqrt{11}\) and \(b=2\), we get \((\sqrt{11})^2-2^2=11-4=7\). Option B (15) is a common mistake from adding 11 and 4 instead of subtracting. Exam tip: recognize conjugates quickly and apply \(a^2-b^2\) to avoid expanding unnecessarily.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
This is a product of conjugates; use the identity \((a+b)(a-b)=a^2-b^2\). With \(a=\sqrt{11}\) and \(b=2\), we get \((\sqrt{11})^2-2^2=11-4=7\). Option B (15) is a common mistake from adding 11 and 4 instead of subtracting. Exam tip: recognize conjugates quickly and apply \(a^2-b^2\) to avoid expanding unnecessarily.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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