Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-8x^2+32=0\)
- \(4(-2x^2+3)=-(13x^2-12)\)
- \(-2(-9x^2+5)=-(-12x^2-476)\)
- \(8x^2+45=5x^2-3\)
- \(4x^2+100=0\)
- \(-5x^2-852=2x^2-5\)
- \(-2x^2+128=0\)
- \(-2(8x^2-4)=-(20x^2-792)\)
- \(-3(10x^2+2)=-(25x^2+851)\)
- \(15x^2-13=8x^2-6\)
- \(3x^2-12=0\)
- \(-8x^2+200=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-8x^2+32=0 \\
\Leftrightarrow -8x^2 = -32 \\
\Leftrightarrow x^2 = \frac{-32}{-8}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(4(-2x^2+3)=-(13x^2-12) \\ \Leftrightarrow -8x^2+12=-13x^2+12 \\
\Leftrightarrow -8x^2+13x^2=12-12 \\
\Leftrightarrow 5x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{5}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-2(-9x^2+5)=-(-12x^2-476) \\ \Leftrightarrow 18x^2-10=12x^2+476 \\
\Leftrightarrow 18x^2-12x^2=476+10 \\
\Leftrightarrow 6x^2 = 486 \\
\Leftrightarrow x^2 = \frac{486}{6}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(8x^2+45=5x^2-3 \\ \Leftrightarrow 8x^2-5x^2=-3-45 \\
\Leftrightarrow 3x^2 = -48 \\
\Leftrightarrow x^2 = \frac{-48}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2+100=0 \\
\Leftrightarrow 4x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(-5x^2-852=2x^2-5 \\ \Leftrightarrow -5x^2-2x^2=-5+852 \\
\Leftrightarrow -7x^2 = 847 \\
\Leftrightarrow x^2 = \frac{847}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2+128=0 \\
\Leftrightarrow -2x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-2}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-2(8x^2-4)=-(20x^2-792) \\ \Leftrightarrow -16x^2+8=-20x^2+792 \\
\Leftrightarrow -16x^2+20x^2=792-8 \\
\Leftrightarrow 4x^2 = 784 \\
\Leftrightarrow x^2 = \frac{784}{4}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-3(10x^2+2)=-(25x^2+851) \\ \Leftrightarrow -30x^2-6=-25x^2-851 \\
\Leftrightarrow -30x^2+25x^2=-851+6 \\
\Leftrightarrow -5x^2 = -845 \\
\Leftrightarrow x^2 = \frac{-845}{-5}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(15x^2-13=8x^2-6 \\ \Leftrightarrow 15x^2-8x^2=-6+13 \\
\Leftrightarrow 7x^2 = 7 \\
\Leftrightarrow x^2 = \frac{7}{7}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(3x^2-12=0 \\
\Leftrightarrow 3x^2 = 12 \\
\Leftrightarrow x^2 = \frac{12}{3}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-8x^2+200=0 \\
\Leftrightarrow -8x^2 = -200 \\
\Leftrightarrow x^2 = \frac{-200}{-8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)