Final Answer:
The value of (u - t)(u^2 - t^2) is 30. To find the value of (u - t)(u^2 - t^2), first, recognize the equations provided: u + t = 5 and u - t = 2. Using these equations, solve for u and t separately.
Step-by-step explanation:
Given u + t = 5 and u - t = 2, we can solve these equations simultaneously to find the values of u and t. Adding the equations together eliminates t: (u + t) + (u - t) = 5 + 2, which simplifies to 2u = 7, and u = 7/2. Subtracting the second equation from the first eliminates u: (u + t) - (u - t) = 5 - 2, simplifying to 2t = 3, and t = 3/2.
Now that we have the values of u and t, we can find (u^2 - t^2). Substitute u = 7/2 and t = 3/2 into the equation to get (u^2 - t^2) = (7/2)^2 - (3/2)^2 = 49/4 - 9/4 = 40/4 = 10.
Finally, multiply (u - t) by (u^2 - t^2): (u - t)(u^2 - t^2) = (2)(10) = 20.
Therefore, the value of (u - t)(u^2 - t^2) is 20.