Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(-4(3x^2-5)=-(13x^2-19)\)
- \(4(9x^2+9)=-(-38x^2+126)\)
- \(8x^2+8=0\)
- \(5(-4x^2+5)=-(25x^2+100)\)
- \(x^2-16=0\)
- \(6x^2+68=10x^2+4\)
- \(-3x^2+112=-4x^2-9\)
- \(-7x^2-252=0\)
- \(-11x^2+1193=-4x^2+10\)
- \(10x^2-385=8x^2+7\)
- \(2(-3x^2-2)=-(4x^2+454)\)
- \(16x^2-1354=10x^2-4\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(-4(3x^2-5)=-(13x^2-19) \\ \Leftrightarrow -12x^2+20=-13x^2+19 \\
\Leftrightarrow -12x^2+13x^2=19-20 \\
\Leftrightarrow x^2 = -1 \\
\Leftrightarrow x^2 = \frac{-1}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(4(9x^2+9)=-(-38x^2+126) \\ \Leftrightarrow 36x^2+36=38x^2-126 \\
\Leftrightarrow 36x^2-38x^2=-126-36 \\
\Leftrightarrow -2x^2 = -162 \\
\Leftrightarrow x^2 = \frac{-162}{-2}=81 \\
\Leftrightarrow x = 9 \vee x = -9 \\
V = \Big\{-9, 9 \Big\} \\ -----------------\)
- \(8x^2+8=0 \\
\Leftrightarrow 8x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-4x^2+5)=-(25x^2+100) \\ \Leftrightarrow -20x^2+25=-25x^2-100 \\
\Leftrightarrow -20x^2+25x^2=-100-25 \\
\Leftrightarrow 5x^2 = -125 \\
\Leftrightarrow x^2 = \frac{-125}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(x^2-16=0 \\
\Leftrightarrow x^2 = 16 \\
\Leftrightarrow x^2 = \frac{16}{1}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(6x^2+68=10x^2+4 \\ \Leftrightarrow 6x^2-10x^2=4-68 \\
\Leftrightarrow -4x^2 = -64 \\
\Leftrightarrow x^2 = \frac{-64}{-4}=16 \\
\Leftrightarrow x = 4 \vee x = -4 \\
V = \Big\{-4, 4 \Big\} \\ -----------------\)
- \(-3x^2+112=-4x^2-9 \\ \Leftrightarrow -3x^2+4x^2=-9-112 \\
\Leftrightarrow x^2 = -121 \\
\Leftrightarrow x^2 = \frac{-121}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-252=0 \\
\Leftrightarrow -7x^2 = 252 \\
\Leftrightarrow x^2 = \frac{252}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(-11x^2+1193=-4x^2+10 \\ \Leftrightarrow -11x^2+4x^2=10-1193 \\
\Leftrightarrow -7x^2 = -1183 \\
\Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\
\Leftrightarrow x = 13 \vee x = -13 \\
V = \Big\{-13, 13 \Big\} \\ -----------------\)
- \(10x^2-385=8x^2+7 \\ \Leftrightarrow 10x^2-8x^2=7+385 \\
\Leftrightarrow 2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{2}=196 \\
\Leftrightarrow x = 14 \vee x = -14 \\
V = \Big\{-14, 14 \Big\} \\ -----------------\)
- \(2(-3x^2-2)=-(4x^2+454) \\ \Leftrightarrow -6x^2-4=-4x^2-454 \\
\Leftrightarrow -6x^2+4x^2=-454+4 \\
\Leftrightarrow -2x^2 = -450 \\
\Leftrightarrow x^2 = \frac{-450}{-2}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(16x^2-1354=10x^2-4 \\ \Leftrightarrow 16x^2-10x^2=-4+1354 \\
\Leftrightarrow 6x^2 = 1350 \\
\Leftrightarrow x^2 = \frac{1350}{6}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)