Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(3(-2x^2-9)=-(13x^2+27)\)
- \(-3x^2-432=0\)
- \(7x^2+1183=0\)
- \(2(10x^2-7)=-(-15x^2-486)\)
- \(6x^2-1350=0\)
- \(-x^2+100=0\)
- \(-6x^2+96=0\)
- \(5x^2+4=2x^2+7\)
- \(-7x^2-674=-3x^2+2\)
- \(3(2x^2-3)=-(-12x^2-1167)\)
- \(4(-9x^2-5)=-(40x^2-16)\)
- \(-4(8x^2-6)=-(36x^2+460)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(3(-2x^2-9)=-(13x^2+27) \\ \Leftrightarrow -6x^2-27=-13x^2-27 \\
\Leftrightarrow -6x^2+13x^2=-27+27 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-3x^2-432=0 \\
\Leftrightarrow -3x^2 = 432 \\
\Leftrightarrow x^2 = \frac{432}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2+1183=0 \\
\Leftrightarrow 7x^2 = -1183 \\
\Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(10x^2-7)=-(-15x^2-486) \\ \Leftrightarrow 20x^2-14=15x^2+486 \\
\Leftrightarrow 20x^2-15x^2=486+14 \\
\Leftrightarrow 5x^2 = 500 \\
\Leftrightarrow x^2 = \frac{500}{5}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(6x^2-1350=0 \\
\Leftrightarrow 6x^2 = 1350 \\
\Leftrightarrow x^2 = \frac{1350}{6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-x^2+100=0 \\
\Leftrightarrow -x^2 = -100 \\
\Leftrightarrow x^2 = \frac{-100}{-1}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(-6x^2+96=0 \\
\Leftrightarrow -6x^2 = -96 \\
\Leftrightarrow x^2 = \frac{-96}{-6}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(5x^2+4=2x^2+7 \\ \Leftrightarrow 5x^2-2x^2=7-4 \\
\Leftrightarrow 3x^2 = 3 \\
\Leftrightarrow x^2 = \frac{3}{3}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-7x^2-674=-3x^2+2 \\ \Leftrightarrow -7x^2+3x^2=2+674 \\
\Leftrightarrow -4x^2 = 676 \\
\Leftrightarrow x^2 = \frac{676}{-4} < 0 \\
V = \varnothing \\ -----------------\)
- \(3(2x^2-3)=-(-12x^2-1167) \\ \Leftrightarrow 6x^2-9=12x^2+1167 \\
\Leftrightarrow 6x^2-12x^2=1167+9 \\
\Leftrightarrow -6x^2 = 1176 \\
\Leftrightarrow x^2 = \frac{1176}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(-9x^2-5)=-(40x^2-16) \\ \Leftrightarrow -36x^2-20=-40x^2+16 \\
\Leftrightarrow -36x^2+40x^2=16+20 \\
\Leftrightarrow 4x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{4}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(-4(8x^2-6)=-(36x^2+460) \\ \Leftrightarrow -32x^2+24=-36x^2-460 \\
\Leftrightarrow -32x^2+36x^2=-460-24 \\
\Leftrightarrow 4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{4} < 0 \\
V = \varnothing \\ -----------------\)