Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-5(5x^2+3)=-(32x^2-97)\)
- \(5(-4x^2+5)=-(25x^2+100)\)
- \(-2x^2+0=0\)
- \(5(-8x^2+5)=-(34x^2+269)\)
- \(3x^2+296=-5x^2+8\)
- \(7x^2-252=2x^2-7\)
- \(6x^2+0=0\)
- \(-3(4x^2+7)=-(9x^2-567)\)
- \(5x^2+353=2x^2-10\)
- \(-12x^2+355=-9x^2-8\)
- \(-5(2x^2+9)=-(11x^2+41)\)
- \(6x^2+864=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-5(5x^2+3)=-(32x^2-97) \\ \Leftrightarrow -25x^2-15=-32x^2+97 \\
\Leftrightarrow -25x^2+32x^2=97+15 \\
\Leftrightarrow 7x^2 = 112 \\
\Leftrightarrow x^2 = \frac{112}{7}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(5(-4x^2+5)=-(25x^2+100) \\ \Leftrightarrow -20x^2+25=-25x^2-100 \\
\Leftrightarrow -20x^2+25x^2=-100-25 \\
\Leftrightarrow 5x^2 = -125 \\
\Leftrightarrow x^2 = \frac{-125}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2+0=0 \\
\Leftrightarrow -2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(-8x^2+5)=-(34x^2+269) \\ \Leftrightarrow -40x^2+25=-34x^2-269 \\
\Leftrightarrow -40x^2+34x^2=-269-25 \\
\Leftrightarrow -6x^2 = -294 \\
\Leftrightarrow x^2 = \frac{-294}{-6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(3x^2+296=-5x^2+8 \\ \Leftrightarrow 3x^2+5x^2=8-296 \\
\Leftrightarrow 8x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2-252=2x^2-7 \\ \Leftrightarrow 7x^2-2x^2=-7+252 \\
\Leftrightarrow 5x^2 = 245 \\
\Leftrightarrow x^2 = \frac{245}{5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(6x^2+0=0 \\
\Leftrightarrow 6x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{6}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3(4x^2+7)=-(9x^2-567) \\ \Leftrightarrow -12x^2-21=-9x^2+567 \\
\Leftrightarrow -12x^2+9x^2=567+21 \\
\Leftrightarrow -3x^2 = 588 \\
\Leftrightarrow x^2 = \frac{588}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2+353=2x^2-10 \\ \Leftrightarrow 5x^2-2x^2=-10-353 \\
\Leftrightarrow 3x^2 = -363 \\
\Leftrightarrow x^2 = \frac{-363}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-12x^2+355=-9x^2-8 \\ \Leftrightarrow -12x^2+9x^2=-8-355 \\
\Leftrightarrow -3x^2 = -363 \\
\Leftrightarrow x^2 = \frac{-363}{-3}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-5(2x^2+9)=-(11x^2+41) \\ \Leftrightarrow -10x^2-45=-11x^2-41 \\
\Leftrightarrow -10x^2+11x^2=-41+45 \\
\Leftrightarrow x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{1}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(6x^2+864=0 \\
\Leftrightarrow 6x^2 = -864 \\
\Leftrightarrow x^2 = \frac{-864}{6} < 0 \\
V = \varnothing \\ -----------------\)