Which of the following is the value of the product (1+\sqrt{3})(1-\sqrt{3})?
Answer and explanation
Correct answer: -2
Use the conjugate-product identity:
\((1+\sqrt{3})(1-\sqrt{3})=1^2-(\sqrt{3})^2=1-3=-2.\)
This follows from \((a+b)(a-b)=a^2-b^2\). The tempting wrong choice 4 comes from incorrectly adding 1 and 3 instead of subtracting. Exam tip: apply the conjugate formula and watch the signs carefully when multiplying surds.
Frequently asked questions
What is the correct answer to this question?
-2
Why is this the correct answer?
Use the conjugate-product identity:
\((1+\sqrt{3})(1-\sqrt{3})=1^2-(\sqrt{3})^2=1-3=-2.\)
This follows from \((a+b)(a-b)=a^2-b^2\). The tempting wrong choice 4 comes from incorrectly adding 1 and 3 instead of subtracting. Exam tip: apply the conjugate formula and watch the signs carefully when multiplying surds.
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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