Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(11x^2+194=8x^2+2\)
- \(-13x^2+774=-9x^2-10\)
- \(-5x^2+970=3x^2+2\)
- \(6x^2-486=0\)
- \(8x^2+9=6x^2+9\)
- \(5(5x^2+7)=-(-23x^2+37)\)
- \(8x^2-288=0\)
- \(8x^2+69=5x^2-6\)
- \(5x^2-605=0\)
- \(-4(2x^2+5)=-(11x^2+32)\)
- \(7x^2-1008=0\)
- \(-8x^2+1568=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(11x^2+194=8x^2+2 \\ \Leftrightarrow 11x^2-8x^2=2-194 \\
\Leftrightarrow 3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-13x^2+774=-9x^2-10 \\ \Leftrightarrow -13x^2+9x^2=-10-774 \\
\Leftrightarrow -4x^2 = -784 \\
\Leftrightarrow x^2 = \frac{-784}{-4}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-5x^2+970=3x^2+2 \\ \Leftrightarrow -5x^2-3x^2=2-970 \\
\Leftrightarrow -8x^2 = -968 \\
\Leftrightarrow x^2 = \frac{-968}{-8}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(6x^2-486=0 \\
\Leftrightarrow 6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(8x^2+9=6x^2+9 \\ \Leftrightarrow 8x^2-6x^2=9-9 \\
\Leftrightarrow 2x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{2}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(5x^2+7)=-(-23x^2+37) \\ \Leftrightarrow 25x^2+35=23x^2-37 \\
\Leftrightarrow 25x^2-23x^2=-37-35 \\
\Leftrightarrow 2x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2-288=0 \\
\Leftrightarrow 8x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{8}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(8x^2+69=5x^2-6 \\ \Leftrightarrow 8x^2-5x^2=-6-69 \\
\Leftrightarrow 3x^2 = -75 \\
\Leftrightarrow x^2 = \frac{-75}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-605=0 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-4(2x^2+5)=-(11x^2+32) \\ \Leftrightarrow -8x^2-20=-11x^2-32 \\
\Leftrightarrow -8x^2+11x^2=-32+20 \\
\Leftrightarrow 3x^2 = -12 \\
\Leftrightarrow x^2 = \frac{-12}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2-1008=0 \\
\Leftrightarrow 7x^2 = 1008 \\
\Leftrightarrow x^2 = \frac{1008}{7}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-8x^2+1568=0 \\
\Leftrightarrow -8x^2 = -1568 \\
\Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)