Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3x^2+192=0\)
- \(-5x^2+980=0\)
- \(-4(-4x^2+10)=-(-17x^2+209)\)
- \(6x^2+9=9x^2+9\)
- \(-11x^2+57=-7x^2-7\)
- \(4(7x^2-7)=-(-29x^2+32)\)
- \(2(-4x^2+10)=-(9x^2+205)\)
- \(4(-9x^2-9)=-(30x^2+132)\)
- \(-10x^2-898=-6x^2+2\)
- \(-7x^2-63=0\)
- \(15x^2-840=8x^2+7\)
- \(-2x^2-75=3x^2+5\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3x^2+192=0 \\
\Leftrightarrow -3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{-3}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-5x^2+980=0 \\
\Leftrightarrow -5x^2 = -980 \\
\Leftrightarrow x^2 = \frac{-980}{-5}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-4(-4x^2+10)=-(-17x^2+209) \\ \Leftrightarrow 16x^2-40=17x^2-209 \\
\Leftrightarrow 16x^2-17x^2=-209+40 \\
\Leftrightarrow -x^2 = -169 \\
\Leftrightarrow x^2 = \frac{-169}{-1}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(6x^2+9=9x^2+9 \\ \Leftrightarrow 6x^2-9x^2=9-9 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-11x^2+57=-7x^2-7 \\ \Leftrightarrow -11x^2+7x^2=-7-57 \\
\Leftrightarrow -4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(4(7x^2-7)=-(-29x^2+32) \\ \Leftrightarrow 28x^2-28=29x^2-32 \\
\Leftrightarrow 28x^2-29x^2=-32+28 \\
\Leftrightarrow -x^2 = -4 \\
\Leftrightarrow x^2 = \frac{-4}{-1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(2(-4x^2+10)=-(9x^2+205) \\ \Leftrightarrow -8x^2+20=-9x^2-205 \\
\Leftrightarrow -8x^2+9x^2=-205-20 \\
\Leftrightarrow x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(-9x^2-9)=-(30x^2+132) \\ \Leftrightarrow -36x^2-36=-30x^2-132 \\
\Leftrightarrow -36x^2+30x^2=-132+36 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-10x^2-898=-6x^2+2 \\ \Leftrightarrow -10x^2+6x^2=2+898 \\
\Leftrightarrow -4x^2 = 900 \\
\Leftrightarrow x^2 = \frac{900}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-63=0 \\
\Leftrightarrow -7x^2 = 63 \\
\Leftrightarrow x^2 = \frac{63}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(15x^2-840=8x^2+7 \\ \Leftrightarrow 15x^2-8x^2=7+840 \\
\Leftrightarrow 7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{7}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-2x^2-75=3x^2+5 \\ \Leftrightarrow -2x^2-3x^2=5+75 \\
\Leftrightarrow -5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{-5} < 0 \\
V = \varnothing \\ -----------------\)