Los exact op.
3p
\(6 - 8 \sqrt{x} = 2\)
○
(Isoleren)
\(-8 \sqrt{x} = -4\)
1p
○
(Kwadrateren)
\((-8 \sqrt{x})^{2} = (-4)^{2}\)
\(64 x = 16\)
\(x = \frac{1}{4}\)
1p
○
(Controleren)
\(x = \frac{1}{4}\) voldoet.
1p
Los exact op.
3p
\(x = \sqrt{-4 x + 45}\)
○
(Kwadrateren)
\(x^{2} = -4 x + 45\)
1p
○
(Oplossen)
\(x^{2} + 4 x - 45 = 0\)
\((x + 9) (x - 5) = 0\)
\(x = -9 ∨ x = 5\)
1p
○
(Controleren)
\(x = -9\) voldoet niet, \(x = 5\) voldoet.
1p
Los exact op.
4p
\(x = \sqrt{2 x + 19} - 2\)
○
(Isoleren)
\(x + 2 = \sqrt{2 x + 19}\)
1p
○
(Kwadrateren)
\((x + 2)^{2} = (\sqrt{2 x + 19})^{2}\)
\(x^{2} + 4 x + 4 = 2 x + 19\)
1p
○
(Oplossen)
\(x^{2} + 2 x - 15 = 0\)
\((x + 5) (x - 3) = 0\)
\(x = -5 ∨ x = 3\)
1p
○
(Controleren)
\(x = -5\) voldoet niet, \(x = 3\) voldoet.
1p
Los exact op.
4p
\(-2 x - 3 \sqrt{x} = -5\)
○
(Isoleren)
\(-2 x + 5 = 3 \sqrt{x}\)
1p
○
(Kwadrateren)
\((-2 x + 5)^{2} = (3 \sqrt{x})^{2}\)
\(4 x^{2} - 20 x + 25 = 9 x\)
1p
○
(Oplossen)
\(4 x^{2} - 29 x + 25 = 0\)
\(D = (-29)^{2} - 4 ⋅ 4 ⋅ 25 = 441\)
\(x = {29 - \sqrt{441} \over 2 ⋅ 4} ∨ x = {29 + \sqrt{441} \over 2 ⋅ 4}\)
\(x = 1 ∨ x = 6\frac{1}{4}\)
1p
○
(Controleren)
\(x = 1\) voldoet, \(x = 6\frac{1}{4}\) voldoet niet.
1p
Los exact op.
4p
\(3 x - 2 \sqrt{3 x - 8} = 8\)
○
(Isoleren)
\(3 x - 8 = 2 \sqrt{3 x - 8}\)
1p
○
(Kwadrateren)
\((3 x - 8)^{2} = (2 \sqrt{3 x - 8})^{2}\)
\(9 x^{2} - 48 x + 64 = 4 ⋅ (3 x - 8)\)
\(9 x^{2} - 48 x + 64 = 12 x - 32\)
1p
○
(Oplossen)
\(9 x^{2} - 60 x + 96 = 0\)
\(3 x^{2} - 20 x + 32 = 0\)
\(D = (-20)^{2} - 4 ⋅ 3 ⋅ 32 = 16\)
\(x = {20 - \sqrt{16} \over 2 ⋅ 3} ∨ x = {20 + \sqrt{16} \over 2 ⋅ 3}\)
\(x = 2\frac{2}{3} ∨ x = 4\)
1p
○
(Controleren)
Beide oplossingen voldoen.
1p