Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2(-2x^2-4)=-(-7x^2-5)\)
- \(-4x^2+900=0\)
- \(11x^2+4=4x^2+4\)
- \(-16x^2+457=-9x^2+9\)
- \(8x^2+648=0\)
- \(7x^2-259=3x^2-3\)
- \(x^2-1345=9x^2+7\)
- \(-3x^2+145=-6x^2-2\)
- \(-2(-6x^2+9)=-(-10x^2-320)\)
- \(6x^2+190=9x^2-2\)
- \(-5x^2+850=2x^2+3\)
- \(x^2+21=8x^2-7\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2(-2x^2-4)=-(-7x^2-5) \\ \Leftrightarrow 4x^2+8=7x^2+5 \\
\Leftrightarrow 4x^2-7x^2=5-8 \\
\Leftrightarrow -3x^2 = -3 \\
\Leftrightarrow x^2 = \frac{-3}{-3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-4x^2+900=0 \\
\Leftrightarrow -4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{-4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(11x^2+4=4x^2+4 \\ \Leftrightarrow 11x^2-4x^2=4-4 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-16x^2+457=-9x^2+9 \\ \Leftrightarrow -16x^2+9x^2=9-457 \\
\Leftrightarrow -7x^2 = -448 \\
\Leftrightarrow x^2 = \frac{-448}{-7}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(8x^2+648=0 \\
\Leftrightarrow 8x^2 = -648 \\
\Leftrightarrow x^2 = \frac{-648}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2-259=3x^2-3 \\ \Leftrightarrow 7x^2-3x^2=-3+259 \\
\Leftrightarrow 4x^2 = 256 \\
\Leftrightarrow x^2 = \frac{256}{4}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(x^2-1345=9x^2+7 \\ \Leftrightarrow x^2-9x^2=7+1345 \\
\Leftrightarrow -8x^2 = 1352 \\
\Leftrightarrow x^2 = \frac{1352}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3x^2+145=-6x^2-2 \\ \Leftrightarrow -3x^2+6x^2=-2-145 \\
\Leftrightarrow 3x^2 = -147 \\
\Leftrightarrow x^2 = \frac{-147}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(-6x^2+9)=-(-10x^2-320) \\ \Leftrightarrow 12x^2-18=10x^2+320 \\
\Leftrightarrow 12x^2-10x^2=320+18 \\
\Leftrightarrow 2x^2 = 338 \\
\Leftrightarrow x^2 = \frac{338}{2}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(6x^2+190=9x^2-2 \\ \Leftrightarrow 6x^2-9x^2=-2-190 \\
\Leftrightarrow -3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{-3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-5x^2+850=2x^2+3 \\ \Leftrightarrow -5x^2-2x^2=3-850 \\
\Leftrightarrow -7x^2 = -847 \\
\Leftrightarrow x^2 = \frac{-847}{-7}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(x^2+21=8x^2-7 \\ \Leftrightarrow x^2-8x^2=-7-21 \\
\Leftrightarrow -7x^2 = -28 \\
\Leftrightarrow x^2 = \frac{-28}{-7}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)