If x = √2 + √3, what is the correct form of x²?
Answer and explanation
Correct answer: 5 + 2√6
This item uses the identity (a + b)² = a² + 2ab + b². Taking a = √2 and b = √3, we obtain x² = (√2 + √3)² = (√2)² + 2(√2)(√3) + (√3)². The first and last terms are 2 and 3, while the middle term is 2√6, because √2 · √3 = √6. Hence x² = 2 + 3 + 2√6 = 5 + 2√6, so option A is correct. Option B omits the factor 2 in the middle term. Option C incorrectly replaces the product by √5, and option D uses incorrect radicands. The middle term is essential.
Frequently asked questions
What is the correct answer to this question?
5 + 2√6
Why is this the correct answer?
This item uses the identity (a + b)² = a² + 2ab + b². Taking a = √2 and b = √3, we obtain x² = (√2 + √3)² = (√2)² + 2(√2)(√3) + (√3)². The first and last terms are 2 and 3, while the middle term is 2√6, because √2 · √3 = √6. Hence x² = 2 + 3 + 2√6 = 5 + 2√6, so option A is correct. Option B omits the factor 2 in the middle term. Option C incorrectly replaces the product by √5, and option D uses incorrect radicands. The middle term is essential.
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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