√(x+7) + √(x-2) =9
x + 7 ≥ 0 ⇒ x ≥ -7
x - 2 ≥ 0 ⇒ x ≥ 2
√(x + 7) = 9 - √(x - 2) |^2
(√(x+7) + √(x - 2) )² = 9²
(√ (x + 7) )² + 2√(x+7) √(x -2) + (√(x - 2))² = 81
x + 7 + 2√(x+7)(x -2) + x - 2 = 81
2x + 5 + 2√(x² + 7x -2x - 14) = 81
2√(x² + 5x - 14) = 81 - 5 - 2x
2√(x² + 5x -14) = 76 - 2x
2√(x² + 5x - 14) = 2(38 - x) |÷2
√(x² + 5x - 14) = 38-x |^2
( √ (x² +5x - 14) )² = (38 - x)²
x² +5x - 14 = 38² - 2*38 *x + x²
x² +5x - 14 = 1444 - 76x + x²
x² + 5x + 76x - x² = 1444 + 14
81x = 1458
x = 1458 ÷ 81
x = 18
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√(18+7) + √(18 -2) = √25 +√16 = 5+4 = 9