Los exact op.
3p
\(8 - 2 \sqrt{x} = 4\)
○
(Isoleren)
\(-2 \sqrt{x} = -4\)
1p
○
(Kwadrateren)
\((-2 \sqrt{x})^{2} = (-4)^{2}\)
\(4 x = 16\)
\(x = 4\)
1p
○
(Controleren)
\(x = 4\) voldoet.
1p
Los exact op.
3p
\(x = \sqrt{-5 x + 24}\)
○
(Kwadrateren)
\(x^{2} = -5 x + 24\)
1p
○
(Oplossen)
\(x^{2} + 5 x - 24 = 0\)
\((x + 8) (x - 3) = 0\)
\(x = -8 ∨ x = 3\)
1p
○
(Controleren)
\(x = -8\) voldoet niet, \(x = 3\) voldoet.
1p
Los exact op.
4p
\(x = \sqrt{6 x + 48} - 8\)
○
(Isoleren)
\(x + 8 = \sqrt{6 x + 48}\)
1p
○
(Kwadrateren)
\((x + 8)^{2} = (\sqrt{6 x + 48})^{2}\)
\(x^{2} + 16 x + 64 = 6 x + 48\)
1p
○
(Oplossen)
\(x^{2} + 10 x + 16 = 0\)
\((x + 8) (x + 2) = 0\)
\(x = -8 ∨ x = -2\)
1p
○
(Controleren)
Beide oplossingen voldoen.
1p
Los exact op.
4p
\(4 x - 4 \sqrt{x} = 3\)
○
(Isoleren)
\(4 x - 3 = 4 \sqrt{x}\)
1p
○
(Kwadrateren)
\((4 x - 3)^{2} = (4 \sqrt{x})^{2}\)
\(16 x^{2} - 24 x + 9 = 16 x\)
1p
○
(Oplossen)
\(16 x^{2} - 40 x + 9 = 0\)
\(D = (-40)^{2} - 4 ⋅ 16 ⋅ 9 = 1\,024\)
\(x = {40 - \sqrt{1\,024} \over 2 ⋅ 16} ∨ x = {40 + \sqrt{1\,024} \over 2 ⋅ 16}\)
\(x = \frac{1}{4} ∨ x = 2\frac{1}{4}\)
1p
○
(Controleren)
\(x = \frac{1}{4}\) voldoet niet, \(x = 2\frac{1}{4}\) voldoet.
1p
Los exact op.
4p
\(2 x - 3 \sqrt{3 x - 3} = 2\)
○
(Isoleren)
\(2 x - 2 = 3 \sqrt{3 x - 3}\)
1p
○
(Kwadrateren)
\((2 x - 2)^{2} = (3 \sqrt{3 x - 3})^{2}\)
\(4 x^{2} - 8 x + 4 = 9 ⋅ (3 x - 3)\)
\(4 x^{2} - 8 x + 4 = 27 x - 27\)
1p
○
(Oplossen)
\(4 x^{2} - 35 x + 31 = 0\)
\(D = (-35)^{2} - 4 ⋅ 4 ⋅ 31 = 729\)
\(x = {35 - \sqrt{729} \over 2 ⋅ 4} ∨ x = {35 + \sqrt{729} \over 2 ⋅ 4}\)
\(x = 1 ∨ x = 7\frac{3}{4}\)
1p
○
(Controleren)
Beide oplossingen voldoen.
1p