Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4(10x^2-9)=-(46x^2-330)\)
- \(2(-4x^2-6)=-(0x^2+524)\)
- \(5(-6x^2+9)=-(26x^2-45)\)
- \(-8x^2+200=0\)
- \(-4(8x^2-6)=-(31x^2+12)\)
- \(8x^2+11=10x^2+3\)
- \(-7x^2-7=0\)
- \(4(-6x^2-6)=-(22x^2-264)\)
- \(-17x^2-443=-10x^2+5\)
- \(x^2+81=0\)
- \(x^2-100=4x^2+8\)
- \(-3(-8x^2-3)=-(-29x^2+236)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4(10x^2-9)=-(46x^2-330) \\ \Leftrightarrow -40x^2+36=-46x^2+330 \\
\Leftrightarrow -40x^2+46x^2=330-36 \\
\Leftrightarrow 6x^2 = 294 \\
\Leftrightarrow x^2 = \frac{294}{6}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(2(-4x^2-6)=-(0x^2+524) \\ \Leftrightarrow -8x^2-12=0x^2-524 \\
\Leftrightarrow -8x^2+0x^2=-524+12 \\
\Leftrightarrow -8x^2 = -512 \\
\Leftrightarrow x^2 = \frac{-512}{-8}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(5(-6x^2+9)=-(26x^2-45) \\ \Leftrightarrow -30x^2+45=-26x^2+45 \\
\Leftrightarrow -30x^2+26x^2=45-45 \\
\Leftrightarrow -4x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-4}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-8x^2+200=0 \\
\Leftrightarrow -8x^2 = -200 \\
\Leftrightarrow x^2 = \frac{-200}{-8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-4(8x^2-6)=-(31x^2+12) \\ \Leftrightarrow -32x^2+24=-31x^2-12 \\
\Leftrightarrow -32x^2+31x^2=-12-24 \\
\Leftrightarrow -x^2 = -36 \\
\Leftrightarrow x^2 = \frac{-36}{-1}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)
- \(8x^2+11=10x^2+3 \\ \Leftrightarrow 8x^2-10x^2=3-11 \\
\Leftrightarrow -2x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{-2}=4 \\
\Leftrightarrow x = 2 \vee x = -2 \\
V = \Big\{-2, 2 \Big\} \\ -----------------\)
- \(-7x^2-7=0 \\
\Leftrightarrow -7x^2 = 7 \\
\Leftrightarrow x^2 = \frac{7}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(-6x^2-6)=-(22x^2-264) \\ \Leftrightarrow -24x^2-24=-22x^2+264 \\
\Leftrightarrow -24x^2+22x^2=264+24 \\
\Leftrightarrow -2x^2 = 288 \\
\Leftrightarrow x^2 = \frac{288}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-17x^2-443=-10x^2+5 \\ \Leftrightarrow -17x^2+10x^2=5+443 \\
\Leftrightarrow -7x^2 = 448 \\
\Leftrightarrow x^2 = \frac{448}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2+81=0 \\
\Leftrightarrow x^2 = -81 \\
\Leftrightarrow x^2 = \frac{-81}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-100=4x^2+8 \\ \Leftrightarrow x^2-4x^2=8+100 \\
\Leftrightarrow -3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-3(-8x^2-3)=-(-29x^2+236) \\ \Leftrightarrow 24x^2+9=29x^2-236 \\
\Leftrightarrow 24x^2-29x^2=-236-9 \\
\Leftrightarrow -5x^2 = -245 \\
\Leftrightarrow x^2 = \frac{-245}{-5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)