Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(6x^2+486=0\)
- \(7x^2+700=0\)
- \(2(2x^2-5)=-(-3x^2+10)\)
- \(5(7x^2-7)=-(-41x^2+131)\)
- \(2(-9x^2-7)=-(10x^2+86)\)
- \(5x^2-5=0\)
- \(-4x^2+16=0\)
- \(17x^2-80=9x^2-8\)
- \(-3(-6x^2-4)=-(-11x^2+835)\)
- \(-8x^2-128=0\)
- \(-3(-5x^2+9)=-(-18x^2+102)\)
- \(-14x^2+733=-8x^2+7\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(6x^2+486=0 \\
\Leftrightarrow 6x^2 = -486 \\
\Leftrightarrow x^2 = \frac{-486}{6} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2+700=0 \\
\Leftrightarrow 7x^2 = -700 \\
\Leftrightarrow x^2 = \frac{-700}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(2x^2-5)=-(-3x^2+10) \\ \Leftrightarrow 4x^2-10=3x^2-10 \\
\Leftrightarrow 4x^2-3x^2=-10+10 \\
\Leftrightarrow x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{1}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(5(7x^2-7)=-(-41x^2+131) \\ \Leftrightarrow 35x^2-35=41x^2-131 \\
\Leftrightarrow 35x^2-41x^2=-131+35 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(2(-9x^2-7)=-(10x^2+86) \\ \Leftrightarrow -18x^2-14=-10x^2-86 \\
\Leftrightarrow -18x^2+10x^2=-86+14 \\
\Leftrightarrow -8x^2 = -72 \\
\Leftrightarrow x^2 = \frac{-72}{-8}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(5x^2-5=0 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-4x^2+16=0 \\
\Leftrightarrow -4x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{-4}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(17x^2-80=9x^2-8 \\ \Leftrightarrow 17x^2-9x^2=-8+80 \\
\Leftrightarrow 8x^2 = 72 \\
\Leftrightarrow x^2 = \frac{72}{8}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-3(-6x^2-4)=-(-11x^2+835) \\ \Leftrightarrow 18x^2+12=11x^2-835 \\
\Leftrightarrow 18x^2-11x^2=-835-12 \\
\Leftrightarrow 7x^2 = -847 \\
\Leftrightarrow x^2 = \frac{-847}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2-128=0 \\
\Leftrightarrow -8x^2 = 128 \\
\Leftrightarrow x^2 = \frac{128}{-8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(-5x^2+9)=-(-18x^2+102) \\ \Leftrightarrow 15x^2-27=18x^2-102 \\
\Leftrightarrow 15x^2-18x^2=-102+27 \\
\Leftrightarrow -3x^2 = -75 \\
\Leftrightarrow x^2 = \frac{-75}{-3}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-14x^2+733=-8x^2+7 \\ \Leftrightarrow -14x^2+8x^2=7-733 \\
\Leftrightarrow -6x^2 = -726 \\
\Leftrightarrow x^2 = \frac{-726}{-6}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)