Problem

If \( X^{3}-Y^{3}=26, X-Y=2 \) then \( X^{2}+X Y+Y^{2}=\cdots \)

Answer

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Answer

5. Substitute X, Y in \(X^2+XY+Y^2\): \(5^2+5(3)+3^2\)

Steps

Step 1 ：1. X=Y+2

Step 2 ：2. Substitute X in \(X^3-Y^3=26\): \((Y+2)^3-Y^3=26\)

Step 3 ：3. Solve for Y: Y=3

Step 4 ：4. Solve for X: X=5

Step 5 ：5. Substitute X, Y in \(X^2+XY+Y^2\): \(5^2+5(3)+3^2\)

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