Multiple choice

Directions: The question is followed by data in the form of two statements labelled as I and II. You must decide whether the data given in the statements are sufficient to answer the question. Using the data, mark your answer as What is the value of x4 + y4 if xy = 1? I. x + y = 5 II. x > 0, y > 0

  1. if statement I alone is sufficient to answer the question

  2. if statement II alone is sufficient to answer the question

  3. if both statements I and II are sufficient to answer the question, but neither statement alone is sufficient

  4. if both statements I and II together are not sufficient to answer the question and additional data is required
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given xy=1 and x+y=5. We need x^4 + y^4. x^2 + y^2 = (x+y)^2 - 2xy = 25 - 2 = 23. x^4 + y^4 = (x^2+y^2)^2 - 2(xy)^2 = 23^2 - 2(1)^2 = 529 - 2 = 527. Statement I is sufficient.

AI explanation

Using the algebraic identity, we can expand (x + y) squared to find that x squared plus y squared equals 25 minus 2, which is 23. Squaring this result gives x to the fourth power plus y to the fourth power plus 2 times x squared times y squared equals 529. Substituting the given value xy = 1 means x squared times y squared is 1, so x to the fourth power plus y to the fourth power equals 529 minus 2, giving a definitive result of 527. Statement I alone provides the required value, making it independently sufficient.

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