Question

For any real number r, which of the following must be greater than r?

Answer 1

C) r^2 + 1 because any number squared (positive or negative) will be positive

Answer 2

An expression is a set of numbers, variables, and mathematical operations. The correct option is C, r² + 1.

What is an Expression?

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

Since real numbers contain positive integers, negative integers, positive decimals, negative decimals, and zero.

Therefore, For any real number r, the expression that will be always greater than r will be (r²+1). This is because,

• √r :- If r=2, then √r will be 1.4142, therefore, √r will be lesser than r.

• 2r :- If r is negative then 2r will also be negative and will be a smaller number than that.

• r² + 1 :- Irrespective of r is negative or positive, decimal or integer, the given expression will be always greater than r.

• r³ + 1 :- If the value of r is negative, then the expression will return a smaller negative number.

Hence, the correct option is C, r² + 1.

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