Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4(5x^2-9)=-(28x^2+92)\)
- \(-4x^2+0=0\)
- \(2(-6x^2+3)=-(15x^2+186)\)
- \(-x^2-4=0\)
- \(-3(7x^2-4)=-(27x^2-36)\)
- \(3(3x^2-9)=-(-15x^2-123)\)
- \(5x^2+70=8x^2-5\)
- \(-5x^2+980=0\)
- \(-x^2-3=4x^2+2\)
- \(4x^2-1560=-4x^2+8\)
- \(3x^2+432=0\)
- \(2x^2-252=4x^2-10\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4(5x^2-9)=-(28x^2+92) \\ \Leftrightarrow -20x^2+36=-28x^2-92 \\
\Leftrightarrow -20x^2+28x^2=-92-36 \\
\Leftrightarrow 8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2+0=0 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(-6x^2+3)=-(15x^2+186) \\ \Leftrightarrow -12x^2+6=-15x^2-186 \\
\Leftrightarrow -12x^2+15x^2=-186-6 \\
\Leftrightarrow 3x^2 = -192 \\
\Leftrightarrow x^2 = \frac{-192}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-x^2-4=0 \\
\Leftrightarrow -x^2 = 4 \\
\Leftrightarrow x^2 = \frac{4}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(7x^2-4)=-(27x^2-36) \\ \Leftrightarrow -21x^2+12=-27x^2+36 \\
\Leftrightarrow -21x^2+27x^2=36-12 \\
\Leftrightarrow 6x^2 = 24 \\
\Leftrightarrow x^2 = \frac{24}{6}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(3(3x^2-9)=-(-15x^2-123) \\ \Leftrightarrow 9x^2-27=15x^2+123 \\
\Leftrightarrow 9x^2-15x^2=123+27 \\
\Leftrightarrow -6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2+70=8x^2-5 \\ \Leftrightarrow 5x^2-8x^2=-5-70 \\
\Leftrightarrow -3x^2 = -75 \\
\Leftrightarrow x^2 = \frac{-75}{-3}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-5x^2+980=0 \\
\Leftrightarrow -5x^2 = -980 \\
\Leftrightarrow x^2 = \frac{-980}{-5}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(-x^2-3=4x^2+2 \\ \Leftrightarrow -x^2-4x^2=2+3 \\
\Leftrightarrow -5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(4x^2-1560=-4x^2+8 \\ \Leftrightarrow 4x^2+4x^2=8+1560 \\
\Leftrightarrow 8x^2 = 1568 \\
\Leftrightarrow x^2 = \frac{1568}{8}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(3x^2+432=0 \\
\Leftrightarrow 3x^2 = -432 \\
\Leftrightarrow x^2 = \frac{-432}{3} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2-252=4x^2-10 \\ \Leftrightarrow 2x^2-4x^2=-10+252 \\
\Leftrightarrow -2x^2 = 242 \\
\Leftrightarrow x^2 = \frac{242}{-2} < 0 \\
V = \varnothing \\ -----------------\)