Which option correctly gives the sum and product of (2+√3) and (2−√3)?
Answer and explanation
Correct answer: Sum 4, product 1
The governing idea is the use of conjugate surds. For the sum, add corresponding terms: (2+√3)+(2−√3)=2+2+√3−√3=4, because the opposite radical terms cancel. For the product, apply (a+b)(a−b)=a²−b²: (2+√3)(2−√3)=2²−(√3)²=4−3=1. Therefore the pair is sum 4 and product 1, so option A is correct. Option B incorrectly treats the sum as zero, while options C and D result from mishandling the radical terms or the difference-of-squares identity.
Frequently asked questions
What is the correct answer to this question?
Sum 4, product 1
Why is this the correct answer?
The governing idea is the use of conjugate surds. For the sum, add corresponding terms: (2+√3)+(2−√3)=2+2+√3−√3=4, because the opposite radical terms cancel. For the product, apply (a+b)(a−b)=a²−b²: (2+√3)(2−√3)=2²−(√3)²=4−3=1. Therefore the pair is sum 4 and product 1, so option A is correct. Option B incorrectly treats the sum as zero, while options C and D result from mishandling the radical terms or the difference-of-squares identity.
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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