Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4(7x^2+7)=-(-22x^2-754)\)
- \(4x^2-2=5x^2+7\)
- \(6x^2-191=5x^2+5\)
- \(6x^2+486=0\)
- \(-7x^2-567=0\)
- \(x^2+81=0\)
- \(-9x^2+186=-8x^2-10\)
- \(3(7x^2-8)=-(-19x^2+26)\)
- \(4x^2-100=0\)
- \(2(5x^2-2)=-(-3x^2-563)\)
- \(x^2-143=4x^2+4\)
- \(3(10x^2+8)=-(-34x^2-40)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4(7x^2+7)=-(-22x^2-754) \\ \Leftrightarrow 28x^2+28=22x^2+754 \\
\Leftrightarrow 28x^2-22x^2=754-28 \\
\Leftrightarrow 6x^2 = 726 \\
\Leftrightarrow x^2 = \frac{726}{6}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(4x^2-2=5x^2+7 \\ \Leftrightarrow 4x^2-5x^2=7+2 \\
\Leftrightarrow -x^2 = 9 \\
\Leftrightarrow x^2 = \frac{9}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(6x^2-191=5x^2+5 \\ \Leftrightarrow 6x^2-5x^2=5+191 \\
\Leftrightarrow x^2 = 196 \\
\Leftrightarrow x^2 = \frac{196}{1}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(6x^2+486=0 \\
\Leftrightarrow 6x^2 = -486 \\
\Leftrightarrow x^2 = \frac{-486}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-567=0 \\
\Leftrightarrow -7x^2 = 567 \\
\Leftrightarrow x^2 = \frac{567}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2+81=0 \\
\Leftrightarrow x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-9x^2+186=-8x^2-10 \\ \Leftrightarrow -9x^2+8x^2=-10-186 \\
\Leftrightarrow -x^2 = -196 \\
\Leftrightarrow x^2 = \frac{-196}{-1}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3(7x^2-8)=-(-19x^2+26) \\ \Leftrightarrow 21x^2-24=19x^2-26 \\
\Leftrightarrow 21x^2-19x^2=-26+24 \\
\Leftrightarrow 2x^2 = -2 \\
\Leftrightarrow x^2 = \frac{-2}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2-100=0 \\
\Leftrightarrow 4x^2 = 100 \\
\Leftrightarrow x^2 = \frac{100}{4}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(2(5x^2-2)=-(-3x^2-563) \\ \Leftrightarrow 10x^2-4=3x^2+563 \\
\Leftrightarrow 10x^2-3x^2=563+4 \\
\Leftrightarrow 7x^2 = 567 \\
\Leftrightarrow x^2 = \frac{567}{7}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(x^2-143=4x^2+4 \\ \Leftrightarrow x^2-4x^2=4+143 \\
\Leftrightarrow -3x^2 = 147 \\
\Leftrightarrow x^2 = \frac{147}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(10x^2+8)=-(-34x^2-40) \\ \Leftrightarrow 30x^2+24=34x^2+40 \\
\Leftrightarrow 30x^2-34x^2=40-24 \\
\Leftrightarrow -4x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{-4} < 0 \\
V = \varnothing \\ -----------------\)