Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2-49=0\)
- \(-5(-7x^2-5)=-(-37x^2-475)\)
- \(-7x^2+898=-3x^2-2\)
- \(-x^2+81=0\)
- \(-3x^2+0=0\)
- \(-17x^2+134=-9x^2+6\)
- \(2x^2+0=0\)
- \(12x^2+329=10x^2-9\)
- \(6x^2-864=0\)
- \(7x^2-250=5x^2-8\)
- \(-4(8x^2-8)=-(33x^2-48)\)
- \(3(-5x^2-10)=-(16x^2+111)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2-49=0 \\
\Leftrightarrow x^2 = 49 \\
\Leftrightarrow x^2 = \frac{49}{1}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-5(-7x^2-5)=-(-37x^2-475) \\ \Leftrightarrow 35x^2+25=37x^2+475 \\
\Leftrightarrow 35x^2-37x^2=475-25 \\
\Leftrightarrow -2x^2 = 450 \\
\Leftrightarrow x^2 = \frac{450}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2+898=-3x^2-2 \\ \Leftrightarrow -7x^2+3x^2=-2-898 \\
\Leftrightarrow -4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{-4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-x^2+81=0 \\
\Leftrightarrow -x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{-1}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-3x^2+0=0 \\
\Leftrightarrow -3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-17x^2+134=-9x^2+6 \\ \Leftrightarrow -17x^2+9x^2=6-134 \\
\Leftrightarrow -8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-8}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2x^2+0=0 \\
\Leftrightarrow 2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(12x^2+329=10x^2-9 \\ \Leftrightarrow 12x^2-10x^2=-9-329 \\
\Leftrightarrow 2x^2 = -338 \\
\Leftrightarrow x^2 = \frac{-338}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-864=0 \\
\Leftrightarrow 6x^2 = 864 \\
\Leftrightarrow x^2 = \frac{864}{6}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(7x^2-250=5x^2-8 \\ \Leftrightarrow 7x^2-5x^2=-8+250 \\
\Leftrightarrow 2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{2}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4(8x^2-8)=-(33x^2-48) \\ \Leftrightarrow -32x^2+32=-33x^2+48 \\
\Leftrightarrow -32x^2+33x^2=48-32 \\
\Leftrightarrow x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(3(-5x^2-10)=-(16x^2+111) \\ \Leftrightarrow -15x^2-30=-16x^2-111 \\
\Leftrightarrow -15x^2+16x^2=-111+30 \\
\Leftrightarrow x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{1} < 0 \\
V = \varnothing \\ -----------------\)