Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(5x^2-134=-3x^2-6\)
- \(-5(-4x^2-5)=-(-17x^2-172)\)
- \(8x^2+128=0\)
- \(-4(5x^2-5)=-(22x^2-28)\)
- \(-2x^2+288=0\)
- \(-4(2x^2-10)=-(7x^2-265)\)
- \(x^2-16=0\)
- \(4(-9x^2-5)=-(32x^2+920)\)
- \(3x^2-384=-5x^2+8\)
- \(8x^2+120=10x^2-8\)
- \(-4x^2+484=0\)
- \(3(-9x^2-5)=-(23x^2+799)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(5x^2-134=-3x^2-6 \\ \Leftrightarrow 5x^2+3x^2=-6+134 \\
\Leftrightarrow 8x^2 = 128 \\
\Leftrightarrow x^2 = \frac{128}{8}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-5(-4x^2-5)=-(-17x^2-172) \\ \Leftrightarrow 20x^2+25=17x^2+172 \\
\Leftrightarrow 20x^2-17x^2=172-25 \\
\Leftrightarrow 3x^2 = 147 \\
\Leftrightarrow x^2 = \frac{147}{3}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(8x^2+128=0 \\
\Leftrightarrow 8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4(5x^2-5)=-(22x^2-28) \\ \Leftrightarrow -20x^2+20=-22x^2+28 \\
\Leftrightarrow -20x^2+22x^2=28-20 \\
\Leftrightarrow 2x^2 = 8 \\
\Leftrightarrow x^2 = \frac{8}{2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-2x^2+288=0 \\
\Leftrightarrow -2x^2 = -288 \\
\Leftrightarrow x^2 = \frac{-288}{-2}=144 \\
\Leftrightarrow x = 12 \vee x = -12 \\
V = \Big\{-12, 12 \Big\} \\ -----------------\)
- \(-4(2x^2-10)=-(7x^2-265) \\ \Leftrightarrow -8x^2+40=-7x^2+265 \\
\Leftrightarrow -8x^2+7x^2=265-40 \\
\Leftrightarrow -x^2 = 225 \\
\Leftrightarrow x^2 = \frac{225}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-16=0 \\
\Leftrightarrow x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(4(-9x^2-5)=-(32x^2+920) \\ \Leftrightarrow -36x^2-20=-32x^2-920 \\
\Leftrightarrow -36x^2+32x^2=-920+20 \\
\Leftrightarrow -4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{-4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(3x^2-384=-5x^2+8 \\ \Leftrightarrow 3x^2+5x^2=8+384 \\
\Leftrightarrow 8x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{8}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(8x^2+120=10x^2-8 \\ \Leftrightarrow 8x^2-10x^2=-8-120 \\
\Leftrightarrow -2x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-2}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-4x^2+484=0 \\
\Leftrightarrow -4x^2 = -484 \\
\Leftrightarrow x^2 = \frac{-484}{-4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(3(-9x^2-5)=-(23x^2+799) \\ \Leftrightarrow -27x^2-15=-23x^2-799 \\
\Leftrightarrow -27x^2+23x^2=-799+15 \\
\Leftrightarrow -4x^2 = -784 \\
\Leftrightarrow x^2 = \frac{-784}{-4}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)