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Solution :-
Q: √(25x - 29) - √(4x - 11) = 3√x
On squaring both sides we get,
=> {√(25x - 29) - √(4x - 11)}² = {3√x}²
=> 25x - 29 + 4x - 11 - 2{√(25x - 29) × √(4x - 11)} = 9x
=> 29x - 40 - 2√(100x² - 275x - 116x + 319) = 9x
=> 29x - 9x - 40 = 2√(100x² - 391x + 319) = 0
=> 20x - 40 = 2√(100x² - 391x + 319)
=> (20x - 40)/2 = √(100x² - 391x + 319)
=> 10x - 20 = √(100x² - 391x + 319)
Again squaring both side,
=> {10x - 20}² = {√(100x² - 391x + 319)}²
=> 100x² + 400 - 400x = 100x² - 391x + 319
=> 100x² - 100x² - 400x + 391x = 319 - 400
=> - 9x = - 81
=> x = - 81/-9 = 9
Hence,
∴ x = 9
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