Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(x^2+977=9x^2+9\)
- \(2(-8x^2+8)=-(11x^2-96)\)
- \(3(-4x^2+4)=-(19x^2-579)\)
- \(3(-3x^2+7)=-(14x^2+1104)\)
- \(-11x^2+593=-8x^2+5\)
- \(4x^2-144=0\)
- \(2(-10x^2+3)=-(26x^2-1182)\)
- \(2x^2-338=0\)
- \(-12x^2-4=-8x^2-4\)
- \(8x^2+281=6x^2-7\)
- \(-4(-3x^2-3)=-(-19x^2+1360)\)
- \(3(10x^2+8)=-(-25x^2-24)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(x^2+977=9x^2+9 \\ \Leftrightarrow x^2-9x^2=9-977 \\
\Leftrightarrow -8x^2 = -968 \\
\Leftrightarrow x^2 = \frac{-968}{-8}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(2(-8x^2+8)=-(11x^2-96) \\ \Leftrightarrow -16x^2+16=-11x^2+96 \\
\Leftrightarrow -16x^2+11x^2=96-16 \\
\Leftrightarrow -5x^2 = 80 \\
\Leftrightarrow x^2 = \frac{80}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(-4x^2+4)=-(19x^2-579) \\ \Leftrightarrow -12x^2+12=-19x^2+579 \\
\Leftrightarrow -12x^2+19x^2=579-12 \\
\Leftrightarrow 7x^2 = 567 \\
\Leftrightarrow x^2 = \frac{567}{7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(3(-3x^2+7)=-(14x^2+1104) \\ \Leftrightarrow -9x^2+21=-14x^2-1104 \\
\Leftrightarrow -9x^2+14x^2=-1104-21 \\
\Leftrightarrow 5x^2 = -1125 \\
\Leftrightarrow x^2 = \frac{-1125}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+593=-8x^2+5 \\ \Leftrightarrow -11x^2+8x^2=5-593 \\
\Leftrightarrow -3x^2 = -588 \\
\Leftrightarrow x^2 = \frac{-588}{-3}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(4x^2-144=0 \\
\Leftrightarrow 4x^2 = 144 \\
\Leftrightarrow x^2 = \frac{144}{4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(2(-10x^2+3)=-(26x^2-1182) \\ \Leftrightarrow -20x^2+6=-26x^2+1182 \\
\Leftrightarrow -20x^2+26x^2=1182-6 \\
\Leftrightarrow 6x^2 = 1176 \\
\Leftrightarrow x^2 = \frac{1176}{6}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(2x^2-338=0 \\
\Leftrightarrow 2x^2 = 338 \\
\Leftrightarrow x^2 = \frac{338}{2}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(-12x^2-4=-8x^2-4 \\ \Leftrightarrow -12x^2+8x^2=-4+4 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(8x^2+281=6x^2-7 \\ \Leftrightarrow 8x^2-6x^2=-7-281 \\
\Leftrightarrow 2x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-3x^2-3)=-(-19x^2+1360) \\ \Leftrightarrow 12x^2+12=19x^2-1360 \\
\Leftrightarrow 12x^2-19x^2=-1360-12 \\
\Leftrightarrow -7x^2 = -1372 \\
\Leftrightarrow x^2 = \frac{-1372}{-7}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(10x^2+8)=-(-25x^2-24) \\ \Leftrightarrow 30x^2+24=25x^2+24 \\
\Leftrightarrow 30x^2-25x^2=24-24 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)