What is the product of (1+\sqrt{7}) and (1-\sqrt{7})?
Answer and explanation
Correct answer: -6
Multiply as conjugates using the identity \\(a+b)(a-b)=a^2-b^2\\. With a=1 and b=\sqrt{7} we get \\(1+\sqrt{7})(1-\sqrt{7})=1^2-(\sqrt{7})^2=1-7=-6\\. Option B (6) is a sign error; C (0) and D (-8) are results of arithmetic mistakes. Exam tip: for conjugate pairs use the difference of squares formula directly to avoid algebraic expansion errors.
Frequently asked questions
What is the correct answer to this question?
-6
Why is this the correct answer?
Multiply as conjugates using the identity \\(a+b)(a-b)=a^2-b^2\\. With a=1 and b=\sqrt{7} we get \\(1+\sqrt{7})(1-\sqrt{7})=1^2-(\sqrt{7})^2=1-7=-6\\. Option B (6) is a sign error; C (0) and D (-8) are results of arithmetic mistakes. Exam tip: for conjugate pairs use the difference of squares formula directly to avoid algebraic expansion errors.
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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