Wortelvergelijkingen
Los exact op.
3p
\(9 - 4 \sqrt{x} = 5\)
○
(Isoleren)
\(-4 \sqrt{x} = -4\)
1p
○
(Kwadrateren)
\((-4 \sqrt{x})^{2} = (-4)^{2}\)
\(16 x = 16\)
\(x = 1\)
1p
○
(Controleren)
\(x = 1\) voldoet.
1p
Los exact op.
3p
\(x = \sqrt{4 x + 45}\)
○
(Kwadrateren)
\(x^{2} = 4 x + 45\)
1p
○
(Oplossen)
\(1 x^{2} + -4 x + -45 = 0\)
\((x + 5) (x + -9) = 0\)
\(x = -5 ∨ x = 9\)
1p
○
(Controleren)
\(x = -5\) voldoet niet, \(x = 9\) voldoet.
1p
Los exact op.
4p
\(x = \sqrt{7 x + 72} - 6\)
○
(Isoleren)
\(x + 6 = \sqrt{7 x + 72}\)
1p
○
(Kwadrateren)
\((x + 6)^{2} = (\sqrt{7 x + 72})^{2}\)
\(x^{2} + 12 x + 36 = 7 x + 72\)
1p
○
(Oplossen)
\(1 x^{2} + 5 x + -36 = 0\)
\((x + 9) (x + -4) = 0\)
\(x = -9 ∨ x = 4\)
1p
○
(Controleren)
\(x = -9\) voldoet niet, \(x = 4\) voldoet.
1p
Los exact op.
4p
\(6 x - 7 \sqrt{x} = -2\)
○
(Isoleren)
\(6 x + 2 = 7 \sqrt{x}\)
1p
○
(Kwadrateren)
\((6 x + 2)^{2} = (7 \sqrt{x})^{2}\)
\(36 x^{2} + 24 x + 4 = 49 x\)
1p
○
(Oplossen)
\(36 x^{2} + -25 x + 4 = 0\)
\(D = -25^{2} - 4 ⋅ 36 ⋅ 4 = 49\)
\(x = {25 - \sqrt{49} \over 2 ⋅ 36} ∨ x = {25 + \sqrt{49} \over 2 ⋅ 36}\)
\(x = {1 \over 4} ∨ x = {4 \over 9}\)
1p
○
(Controleren)
Beide oplossingen voldoen.
1p
Los exact op.
4p
\(2 x - 2 \sqrt{6 x - 2} = 6\)
○
(Isoleren)
\(2 x - 6 = 2 \sqrt{6 x - 2}\)
1p
○
(Kwadrateren)
\((2 x - 6)^{2} = (2 \sqrt{6 x - 2})^{2}\)
\(4 x^{2} - 24 x + 36 = 4 ⋅ (6 x - 2)\)
\(4 x^{2} - 24 x + 36 = 24 x - 8\)
1p
○
(Oplossen)
\(4 x^{2} + -48 x + 44 = 0\)
\(1 x^{2} + -12 x + 11 = 0\)
\((x + -1) (x + -11) = 0\)
\(x = 1 ∨ x = 11\)
1p
○
(Controleren)
\(x = 1\) voldoet niet, \(x = 11\) voldoet.
1p