If 2x + (1/9x) = 5, then find the value of

Solution

Given that, 2x + (1/9x) = 5 Multiplying on both sides by (9/2) 9x + (1/2x) = (45/2) Squaring both sides, we have; {9x + (1/2x)}² = (45/2)² Or, (9x)² + 2 X 9x X (1/2x) + (1/2x)² = (2025/4) Or, 81x² + 9 + (1/4x²) = (2025/4) Or, 81x² + (1/4x²) + 9 - (2025/4) = 0 Or, 81x² + (1/4x²) - (1989/4) = 0 On adding 51 on both sides, we have 81x² + (1/4x²) - (1989/4) + 51 = 51 So, 81x² + (1/4x²) - {(1989 - 204)/4} = 51 Or, 81x² + (1/4x²) - (1785/4) = 51