Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-2x^2+0=0\)
- \(-8x^2+392=0\)
- \(x^2+0=0\)
- \(3(-10x^2-4)=-(33x^2+12)\)
- \(2(10x^2+9)=-(-17x^2-21)\)
- \(7x^2-700=0\)
- \(-6x^2+1176=0\)
- \(-2x^2+32=0\)
- \(x^2+247=3x^2+5\)
- \(2(-5x^2+8)=-(6x^2+560)\)
- \(x^2+1020=-5x^2+6\)
- \(-4(7x^2-2)=-(32x^2-152)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-2x^2+0=0 \\
\Leftrightarrow -2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-8x^2+392=0 \\
\Leftrightarrow -8x^2 = -392 \\
\Leftrightarrow x^2 = \frac{-392}{-8}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(x^2+0=0 \\
\Leftrightarrow x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(3(-10x^2-4)=-(33x^2+12) \\ \Leftrightarrow -30x^2-12=-33x^2-12 \\
\Leftrightarrow -30x^2+33x^2=-12+12 \\
\Leftrightarrow 3x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{3}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(10x^2+9)=-(-17x^2-21) \\ \Leftrightarrow 20x^2+18=17x^2+21 \\
\Leftrightarrow 20x^2-17x^2=21-18 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(7x^2-700=0 \\
\Leftrightarrow 7x^2 = 700 \\
\Leftrightarrow x^2 = \frac{700}{7}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-6x^2+1176=0 \\
\Leftrightarrow -6x^2 = -1176 \\
\Leftrightarrow x^2 = \frac{-1176}{-6}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-2x^2+32=0 \\
\Leftrightarrow -2x^2 = -32 \\
\Leftrightarrow x^2 = \frac{-32}{-2}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(x^2+247=3x^2+5 \\ \Leftrightarrow x^2-3x^2=5-247 \\
\Leftrightarrow -2x^2 = -242 \\
\Leftrightarrow x^2 = \frac{-242}{-2}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(2(-5x^2+8)=-(6x^2+560) \\ \Leftrightarrow -10x^2+16=-6x^2-560 \\
\Leftrightarrow -10x^2+6x^2=-560-16 \\
\Leftrightarrow -4x^2 = -576 \\
\Leftrightarrow x^2 = \frac{-576}{-4}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(x^2+1020=-5x^2+6 \\ \Leftrightarrow x^2+5x^2=6-1020 \\
\Leftrightarrow 6x^2 = -1014 \\
\Leftrightarrow x^2 = \frac{-1014}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(7x^2-2)=-(32x^2-152) \\ \Leftrightarrow -28x^2+8=-32x^2+152 \\
\Leftrightarrow -28x^2+32x^2=152-8 \\
\Leftrightarrow 4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)