Question

Помогите решить:
√(3 х+4)+√(х-4)=2√х

Answer 1

$sqrt{3x+4}+sqrt{x-4} = 2sqrt{x}, \ x geq 4, \ (sqrt{3x+4}+sqrt{x-4})^2 = (2sqrt{x})^2, \ 3x+4+2sqrt{(3x+4)(x-4)}+x-4 = 4x, \ 2sqrt{3x^2-8x-16} = 0, \ sqrt{3x^2-8x-16} = 0, \ 3x^2-8x-16 = 0, \ D_{/4}=(-4)^2-3cdot(-16) = 64 = 8^2, \ x_1 = frac{4-8}{3} = -frac{4}{3} < 4, \ x_2 = frac{4+8}{3} = 4. \ x=4.$