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If (x=1+\sqrt{2}), what is the value of (x^2-2x)?
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Answer and explanation
Correct answer: (1)
Step 1: (x^2-2x=x(x-2)). Step 2: With (x=1+\sqrt{2}), (x-2=\sqrt{2}-1), so the product ((1+\sqrt{2})(\sqrt{2}-1)=1). Step 3: Recognizing conjugate-like forms makes calculation shorter.
Frequently asked questions
What is the correct answer to this question?
(1)
Why is this the correct answer?
Step 1: (x^2-2x=x(x-2)). Step 2: With (x=1+\sqrt{2}), (x-2=\sqrt{2}-1), so the product ((1+\sqrt{2})(\sqrt{2}-1)=1). Step 3: Recognizing conjugate-like forms makes calculation shorter.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Real Numbers. Topic: Irrational numbers.
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