Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-3(4x^2-6)=-(4x^2+110)\)
- \(5x^2+218=4x^2-7\)
- \(2(-10x^2-2)=-(15x^2-1121)\)
- \(-6x^2+6=0\)
- \(-4(-10x^2+4)=-(-41x^2+25)\)
- \(5x^2-245=0\)
- \(-3x^2-243=0\)
- \(-8x^2+0=0\)
- \(-4(4x^2+8)=-(19x^2-268)\)
- \(4(-5x^2-2)=-(28x^2+8)\)
- \(2(-9x^2+8)=-(20x^2+2)\)
- \(-x^2+25=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-3(4x^2-6)=-(4x^2+110) \\ \Leftrightarrow -12x^2+18=-4x^2-110 \\
\Leftrightarrow -12x^2+4x^2=-110-18 \\
\Leftrightarrow -8x^2 = -128 \\
\Leftrightarrow x^2 = \frac{-128}{-8}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(5x^2+218=4x^2-7 \\ \Leftrightarrow 5x^2-4x^2=-7-218 \\
\Leftrightarrow x^2 = -225 \\
\Leftrightarrow x^2 = \frac{-225}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(2(-10x^2-2)=-(15x^2-1121) \\ \Leftrightarrow -20x^2-4=-15x^2+1121 \\
\Leftrightarrow -20x^2+15x^2=1121+4 \\
\Leftrightarrow -5x^2 = 1125 \\
\Leftrightarrow x^2 = \frac{1125}{-5} < 0 \\
V = \varnothing \\ -----------------\)
- \(-6x^2+6=0 \\
\Leftrightarrow -6x^2 = -6 \\
\Leftrightarrow x^2 = \frac{-6}{-6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-4(-10x^2+4)=-(-41x^2+25) \\ \Leftrightarrow 40x^2-16=41x^2-25 \\
\Leftrightarrow 40x^2-41x^2=-25+16 \\
\Leftrightarrow -x^2 = -9 \\
\Leftrightarrow x^2 = \frac{-9}{-1}=9 \\
\Leftrightarrow x = 3 \vee x = -3 \\
V = \Big\{-3, 3 \Big\} \\ -----------------\)
- \(5x^2-245=0 \\
\Leftrightarrow 5x^2 = 245 \\
\Leftrightarrow x^2 = \frac{245}{5}=49 \\
\Leftrightarrow x = 7 \vee x = -7 \\
V = \Big\{-7, 7 \Big\} \\ -----------------\)
- \(-3x^2-243=0 \\
\Leftrightarrow -3x^2 = 243 \\
\Leftrightarrow x^2 = \frac{243}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-8x^2+0=0 \\
\Leftrightarrow -8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{-8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(-4(4x^2+8)=-(19x^2-268) \\ \Leftrightarrow -16x^2-32=-19x^2+268 \\
\Leftrightarrow -16x^2+19x^2=268+32 \\
\Leftrightarrow 3x^2 = 300 \\
\Leftrightarrow x^2 = \frac{300}{3}=100 \\
\Leftrightarrow x = 10 \vee x = -10 \\
V = \Big\{-10, 10 \Big\} \\ -----------------\)
- \(4(-5x^2-2)=-(28x^2+8) \\ \Leftrightarrow -20x^2-8=-28x^2-8 \\
\Leftrightarrow -20x^2+28x^2=-8+8 \\
\Leftrightarrow 8x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{8}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2(-9x^2+8)=-(20x^2+2) \\ \Leftrightarrow -18x^2+16=-20x^2-2 \\
\Leftrightarrow -18x^2+20x^2=-2-16 \\
\Leftrightarrow 2x^2 = -18 \\
\Leftrightarrow x^2 = \frac{-18}{2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-x^2+25=0 \\
\Leftrightarrow -x^2 = -25 \\
\Leftrightarrow x^2 = \frac{-25}{-1}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)