Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-7x^2+847=0\)
- \(5(-5x^2+8)=-(31x^2-526)\)
- \(-4(4x^2+7)=-(15x^2+128)\)
- \(4x^2+77=5x^2-4\)
- \(-9x^2+59=-7x^2+9\)
- \(3(-7x^2+7)=-(18x^2-696)\)
- \(5x^2-980=0\)
- \(3x^2-588=0\)
- \(-5(4x^2-7)=-(17x^2-38)\)
- \(6x^2+864=0\)
- \(2x^2+164=3x^2-5\)
- \(-3x^2+192=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-7x^2+847=0 \\
\Leftrightarrow -7x^2 = -847 \\
\Leftrightarrow x^2 = \frac{-847}{-7}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(5(-5x^2+8)=-(31x^2-526) \\ \Leftrightarrow -25x^2+40=-31x^2+526 \\
\Leftrightarrow -25x^2+31x^2=526-40 \\
\Leftrightarrow 6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-4(4x^2+7)=-(15x^2+128) \\ \Leftrightarrow -16x^2-28=-15x^2-128 \\
\Leftrightarrow -16x^2+15x^2=-128+28 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(4x^2+77=5x^2-4 \\ \Leftrightarrow 4x^2-5x^2=-4-77 \\
\Leftrightarrow -x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{-1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-9x^2+59=-7x^2+9 \\ \Leftrightarrow -9x^2+7x^2=9-59 \\
\Leftrightarrow -2x^2 = -50 \\
\Leftrightarrow x^2 = \frac{-50}{-2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(3(-7x^2+7)=-(18x^2-696) \\ \Leftrightarrow -21x^2+21=-18x^2+696 \\
\Leftrightarrow -21x^2+18x^2=696-21 \\
\Leftrightarrow -3x^2 = 675 \\
\Leftrightarrow x^2 = \frac{675}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-980=0 \\
\Leftrightarrow 5x^2 = 980 \\
\Leftrightarrow x^2 = \frac{980}{5}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3x^2-588=0 \\
\Leftrightarrow 3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-5(4x^2-7)=-(17x^2-38) \\ \Leftrightarrow -20x^2+35=-17x^2+38 \\
\Leftrightarrow -20x^2+17x^2=38-35 \\
\Leftrightarrow -3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2+864=0 \\
\Leftrightarrow 6x^2 = -864 \\
\Leftrightarrow x^2 = \frac{-864}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2+164=3x^2-5 \\ \Leftrightarrow 2x^2-3x^2=-5-164 \\
\Leftrightarrow -x^2 = -169 \\
\Leftrightarrow x^2 = \frac{-169}{-1}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-3x^2+192=0 \\
\Leftrightarrow -3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{-3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)