\require{AMSmath}

Uitwerkingen

a.	$\eqalign{& x - 3\sqrt x = - 2\cr& neem\,\,u = \sqrt x \cr & u^2 - 3u + 2 = 0 \cr & (u - 1)(u - 2) = 0 \cr & u = 1\,\,of\,\,u = 2 \cr & x = 1\,\,of\,\,x = 4 \cr} $	d.	$\eqalign{& 3e^{2x} - e^x - 2 = 0\cr& neem\,\,u = e^x \cr & 3u^2 - u - 2 = 0 \cr & (u - 1)(3u + 2) = 0 \cr & u = 1\,\,of\,\,3u + 2 = 0 \cr & u = 1\,\,of\,\,u = - \frac{2}{3} \cr & e^x = 1\,\,of\,\,e^x = - \frac{2}{3}\,\,(v.n.) \cr & x = 0\, \cr} $
b.	$\eqalign{& \frac{1}{{(x - 1)^2 }} - \frac{1}{{x - 1}} - 2 = 0\cr& neem\,\,u = \frac{1}{{x - 1}} \cr & u^2 - u - 2 = 0 \cr & (u - 2)(u + 1) = 0 \cr & \frac{1}{{x - 1}} = 2\,\,of\,\,\frac{1}{{x - 1}} = - 1 \cr & 2x - 2 = 1\,\,of\,\, - x + 1 = 1 \cr & 2x = 3\,\,of\,\, - x = 0 \cr & x = 1\frac{1}{2}\,\,of\,\,x = 0 \cr} $	e.	$\eqalign{& sin ^2 x - 4sin x - 5 = 0\cr& neem\,\,u = sin x \cr & u^2 - 4u - 5 = 0 \cr & (u - 5)(u + 1) = 0 \cr & u = 5\,\,of\,\,x = - 1 \cr & sin (x) = 5\,\,(v.n.)\,\,of\,\,sin (x) = - 1 \cr & x = 1\frac{1}{2}\pi + k \cdot 2\pi \cr} $
c.	$\eqalign{& - (x + 3)^6 + 4(x + 3)^3 = - 21\cr& neem\,\,u = \left( {x + 3} \right)^3 \cr & - u^2 + 4u + 21 = 0 \cr & u^2 - 4u - 21 = 0 \cr & (u - 7)(u + 3) = 0 \cr & u = 7\,\,of\,\,u = - 3 \cr & (x + 3)^3 = 7\,\,of\,\,(x + 3)^3 = - 3 \cr & x = - 3 + \root 3 \of 7 \,\,of\,\,x = - 3 - \root 3 \of 3 \cr} $

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