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Class 10 Mathematics Polynomials Operations on real numbers and the laws of exponentsMediumLevel 45

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If (x+y=10) and (x^2+y^2=58), what is the value of (xy)?

Answer and explanation

Correct answer: 21

Use the identity ((x+y)^2=x^2+y^2+2xy). Substituting the given values gives (10^2=58+2xy), or (100=58+2xy). Hence (2xy=42) and (xy=21). The value 42 is the value of (2xy), not of (xy). Exam tip: In such questions, square the sum and subtract (x^2+y^2) to find (2xy).

Related tags

Polynomials Algebraic Identities Real Numbers Exponents Mathematical Operations

Frequently asked questions

What is the correct answer to this question?

21

Why is this the correct answer?

Use the identity ((x+y)^2=x^2+y^2+2xy). Substituting the given values gives (10^2=58+2xy), or (100=58+2xy). Hence (2xy=42) and (xy=21). The value 42 is the value of (2xy), not of (xy). Exam tip: In such questions, square the sum and subtract (x^2+y^2) to find (2xy).

Which subject and chapter does this question cover?

This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Operations on real numbers and the laws of exponents.

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