Question
If 2x + (1/9x) = 5, then find the value of
81x2 + (1/4x2) - (1785/4)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
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