Question

Find the value of 125p³ - 8q³ if 5p -2q = 1 and pq = 2

Answer 1

To find the value of 125p³ - 8q³ when given an equation for p and q, substitute the values into the expression and simplify the equation step by step.

Step-by-step explanation:

To find the value of 125p³ - 8q³ when 5p - 2q = 1 and pq = 2, we need to substitute the given equations into the expression.

1. From 5p - 2q = 1, we can isolate 5p by adding 2q to both sides: 5p = 1 + 2q.
2. Then, divide both sides by 5 to solve for p: p = (1 + 2q) / 5.
3. Next, substitute the value of p into the expression to get: 125((1 + 2q) / 5)³ - 8q³.
4. Expand and simplify the expression: (1/125)(1 + 2q)³ - 8q³.
5. Further simplify by expanding the cube: (1/125)(1 + 3(2q) + 3(2q)² + (2q)³) - 8q³.
6. Simplify the expression: (1/125)(1 + 6q + 12q² + 8q³) - 8q³.
7. Combine like terms: (1/125)(1 + 6q + 12q²) - 7q³.
8. We also have pq = 2, so substitute the value of q into the expression: (1/125)(1 + 6(2) + 12(2)²) - 7(2)³.
9. Continue to simplify: (1/125)(1 + 12 + 48) - 56.
10. Further simplify: (1/125)(61) - 56.
11. Finally, calculate the value: (61/125) - 56 ≈ -55.512.

Therefore, the value of 125p³ - 8q³ is approximately -55.512.

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