Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(2(9x^2-10)=-(-20x^2-108)\)
- \(7x^2+175=0\)
- \(2x^2+902=6x^2+2\)
- \(-13x^2-1=-7x^2-7\)
- \(-4(7x^2+2)=-(20x^2+208)\)
- \(2x^2-493=-2x^2-9\)
- \(-7x^2-6=-8x^2-10\)
- \(-x^2-21=6x^2+7\)
- \(5x^2-605=0\)
- \(4(-4x^2-3)=-(21x^2+192)\)
- \(8x^2+8=0\)
- \(-4x^2+144=0\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(2(9x^2-10)=-(-20x^2-108) \\ \Leftrightarrow 18x^2-20=20x^2+108 \\
\Leftrightarrow 18x^2-20x^2=108+20 \\
\Leftrightarrow -2x^2 = 128 \\
\Leftrightarrow x^2 = \frac{128}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(7x^2+175=0 \\
\Leftrightarrow 7x^2 = -175 \\
\Leftrightarrow x^2 = \frac{-175}{7} < 0 \\
V = \varnothing \\ -----------------\)
- \(2x^2+902=6x^2+2 \\ \Leftrightarrow 2x^2-6x^2=2-902 \\
\Leftrightarrow -4x^2 = -900 \\
\Leftrightarrow x^2 = \frac{-900}{-4}=225 \\
\Leftrightarrow x = 15 \vee x = -15 \\
V = \Big\{-15, 15 \Big\} \\ -----------------\)
- \(-13x^2-1=-7x^2-7 \\ \Leftrightarrow -13x^2+7x^2=-7+1 \\
\Leftrightarrow -6x^2 = -6 \\
\Leftrightarrow x^2 = \frac{-6}{-6}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-4(7x^2+2)=-(20x^2+208) \\ \Leftrightarrow -28x^2-8=-20x^2-208 \\
\Leftrightarrow -28x^2+20x^2=-208+8 \\
\Leftrightarrow -8x^2 = -200 \\
\Leftrightarrow x^2 = \frac{-200}{-8}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(2x^2-493=-2x^2-9 \\ \Leftrightarrow 2x^2+2x^2=-9+493 \\
\Leftrightarrow 4x^2 = 484 \\
\Leftrightarrow x^2 = \frac{484}{4}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(-7x^2-6=-8x^2-10 \\ \Leftrightarrow -7x^2+8x^2=-10+6 \\
\Leftrightarrow x^2 = -4 \\
\Leftrightarrow x^2 = \frac{-4}{1} < 0 \\
V = \varnothing \\ -----------------\)
- \(-x^2-21=6x^2+7 \\ \Leftrightarrow -x^2-6x^2=7+21 \\
\Leftrightarrow -7x^2 = 28 \\
\Leftrightarrow x^2 = \frac{28}{-7} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2-605=0 \\
\Leftrightarrow 5x^2 = 605 \\
\Leftrightarrow x^2 = \frac{605}{5}=121 \\
\Leftrightarrow x = 11 \vee x = -11 \\
V = \Big\{-11, 11 \Big\} \\ -----------------\)
- \(4(-4x^2-3)=-(21x^2+192) \\ \Leftrightarrow -16x^2-12=-21x^2-192 \\
\Leftrightarrow -16x^2+21x^2=-192+12 \\
\Leftrightarrow 5x^2 = -180 \\
\Leftrightarrow x^2 = \frac{-180}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(8x^2+8=0 \\
\Leftrightarrow 8x^2 = -8 \\
\Leftrightarrow x^2 = \frac{-8}{8} < 0 \\
V = \varnothing \\ -----------------\)
- \(-4x^2+144=0 \\
\Leftrightarrow -4x^2 = -144 \\
\Leftrightarrow x^2 = \frac{-144}{-4}=36 \\
\Leftrightarrow x = 6 \vee x = -6 \\
V = \Big\{-6, 6 \Big\} \\ -----------------\)