Multiple choice

Solve the following equations: $x^{5} - y^{5} = 992$, $x - y = 2$.

  1. $(2,4)$
  2. $(4,2)$
  3. $(4,3)$
  4. $(-3,-5)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given x - y = 2, we can substitute x = y + 2 into the first equation: (y + 2)^5 - y^5 = 992. Expanding this, we get 10y^4 + 40y^3 + 80y^2 + 80y + 32 = 992. Solving for y, we find y = 2, which gives x = 4.

AI explanation

Let x - y = 2 and x^5 - y^5 = 992; substituting x = y + 2 into the second equation gives (y + 2)^5 - y^5 = 992. Checking the options, if y = 2, then x must be 4. Verifying this pair gives 4^5 - 2^5 = 1024 - 32 = 992, which is correct. Therefore, the solution is the ordered pair (4, 2).

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