Question

resolva:
$\sqrt{2x+3}- \sqrt{7-x}=1$

Answer 1

Ola Kelly

(a - b)² = a² - 2ab + b²

a = √(2x + 3)
b = √(7 - x)

(√(2x + 3) - √(7 - x))² = 1

2x + 3 - 2*√((2x + 3)*(7 - x)) + 7 - x = 1

x + 9 = 2*√((2x + 3)*(7 - x)) 

(x + 9)² = 4*(2x + 3)*(7 - x)

x²  + 18x + 81 = 4*(-2x² + 11x + 21) 

x² + 18x + 81 = -8x² + 44x + 84 

9x² - 26x - 3 = 0 

d² = 26² + 4*3*9 = 784 
d = 28 

x1 = (26 + 28)/18 = 54/18 = 3
x2 = (26 - 28)/18 = -2/18 = -1/9 

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