Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(6x^2-54=0\)
- \(4(-6x^2+9)=-(28x^2-20)\)
- \(14x^2+973=9x^2-7\)
- \(14x^2-396=9x^2+9\)
- \(-3(-5x^2-3)=-(-13x^2-7)\)
- \(-4(-10x^2-4)=-(-43x^2-163)\)
- \(-4(-8x^2+6)=-(-27x^2-1101)\)
- \(-2x^2+297=4x^2+3\)
- \(-3x^2+12=0\)
- \(-3x^2+27=0\)
- \(x^2+239=6x^2-6\)
- \(-2(-2x^2+2)=-(-11x^2+32)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(6x^2-54=0 \\
\Leftrightarrow 6x^2 = 54 \\
\Leftrightarrow x^2 = \frac{54}{6}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(4(-6x^2+9)=-(28x^2-20) \\ \Leftrightarrow -24x^2+36=-28x^2+20 \\
\Leftrightarrow -24x^2+28x^2=20-36 \\
\Leftrightarrow 4x^2 = -16 \\
\Leftrightarrow x^2 = \frac{-16}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(14x^2+973=9x^2-7 \\ \Leftrightarrow 14x^2-9x^2=-7-973 \\
\Leftrightarrow 5x^2 = -980 \\
\Leftrightarrow x^2 = \frac{-980}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(14x^2-396=9x^2+9 \\ \Leftrightarrow 14x^2-9x^2=9+396 \\
\Leftrightarrow 5x^2 = 405 \\
\Leftrightarrow x^2 = \frac{405}{5}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(-3(-5x^2-3)=-(-13x^2-7) \\ \Leftrightarrow 15x^2+9=13x^2+7 \\
\Leftrightarrow 15x^2-13x^2=7-9 \\
\Leftrightarrow 2x^2 = -2 \\
\Leftrightarrow x^2 = \frac{-2}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-10x^2-4)=-(-43x^2-163) \\ \Leftrightarrow 40x^2+16=43x^2+163 \\
\Leftrightarrow 40x^2-43x^2=163-16 \\
\Leftrightarrow -3x^2 = 147 \\
\Leftrightarrow x^2 = \frac{147}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(-8x^2+6)=-(-27x^2-1101) \\ \Leftrightarrow 32x^2-24=27x^2+1101 \\
\Leftrightarrow 32x^2-27x^2=1101+24 \\
\Leftrightarrow 5x^2 = 1125 \\
\Leftrightarrow x^2 = \frac{1125}{5}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-2x^2+297=4x^2+3 \\ \Leftrightarrow -2x^2-4x^2=3-297 \\
\Leftrightarrow -6x^2 = -294 \\
\Leftrightarrow x^2 = \frac{-294}{-6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-3x^2+12=0 \\
\Leftrightarrow -3x^2 = -12 \\
\Leftrightarrow x^2 = \frac{-12}{-3}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-3x^2+27=0 \\
\Leftrightarrow -3x^2 = -27 \\
\Leftrightarrow x^2 = \frac{-27}{-3}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(x^2+239=6x^2-6 \\ \Leftrightarrow x^2-6x^2=-6-239 \\
\Leftrightarrow -5x^2 = -245 \\
\Leftrightarrow x^2 = \frac{-245}{-5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-2(-2x^2+2)=-(-11x^2+32) \\ \Leftrightarrow 4x^2-4=11x^2-32 \\
\Leftrightarrow 4x^2-11x^2=-32+4 \\
\Leftrightarrow -7x^2 = -28 \\
\Leftrightarrow x^2 = \frac{-28}{-7}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)