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The number xx is irrational. Which statement about 2+x2 + x is true?\newlineChoices:\newline(A) 2+x2 + x is rational.\newline(B) 2+x2 + x is irrational.\newline(C) 2+x2 + x can be rational or irrational, depending on the value of xx.

Full solution

Q. The number xx is irrational. Which statement about 2+x2 + x is true?\newlineChoices:\newline(A) 2+x2 + x is rational.\newline(B) 2+x2 + x is irrational.\newline(C) 2+x2 + x can be rational or irrational, depending on the value of xx.
  1. Identify Number 22: Identify the nature of the number 22. 22 is a rational number because it can be expressed as a fraction of two integers (2/1)(2/1).
  2. Understand Number xx: Understand the nature of the number xx.xx is given as an irrational number, which means it cannot be expressed as a fraction of two integers.
  3. Analyze Sum: Analyze the sum of a rational number and an irrational number.\newlineAdding a rational number to an irrational number results in an irrational number. This is because the sum cannot be expressed as a fraction of two integers.
  4. Apply Analysis: Apply the analysis to the given problem.\newlineSince 22 is rational and xx is irrational, the sum 2+x2 + x is irrational.

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