Los de vierkantsvergelijking op zonder de discriminant te gebruiken
- \(4x^2+576=0\)
- \(12x^2-54=10x^2-4\)
- \(-3x^2-108=0\)
- \(-2(2x^2+6)=-(9x^2-308)\)
- \(3(-2x^2-7)=-(13x^2+21)\)
- \(2x^2-34=3x^2+2\)
- \(5x^2+320=0\)
- \(5(-10x^2+5)=-(44x^2-175)\)
- \(-2x^2-392=0\)
- \(-7x^2-10=-8x^2-9\)
- \(-3(-9x^2-4)=-(-35x^2+500)\)
- \(-2(10x^2+6)=-(25x^2+7)\)
Los de vierkantsvergelijking op zonder de discriminant te gebruiken
Verbetersleutel
- \(4x^2+576=0 \\
\Leftrightarrow 4x^2 = -576 \\
\Leftrightarrow x^2 = \frac{-576}{4} < 0 \\
V = \varnothing \\ -----------------\)
- \(12x^2-54=10x^2-4 \\ \Leftrightarrow 12x^2-10x^2=-4+54 \\
\Leftrightarrow 2x^2 = 50 \\
\Leftrightarrow x^2 = \frac{50}{2}=25 \\
\Leftrightarrow x = 5 \vee x = -5 \\
V = \Big\{-5, 5 \Big\} \\ -----------------\)
- \(-3x^2-108=0 \\
\Leftrightarrow -3x^2 = 108 \\
\Leftrightarrow x^2 = \frac{108}{-3} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2(2x^2+6)=-(9x^2-308) \\ \Leftrightarrow -4x^2-12=-9x^2+308 \\
\Leftrightarrow -4x^2+9x^2=308+12 \\
\Leftrightarrow 5x^2 = 320 \\
\Leftrightarrow x^2 = \frac{320}{5}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(3(-2x^2-7)=-(13x^2+21) \\ \Leftrightarrow -6x^2-21=-13x^2-21 \\
\Leftrightarrow -6x^2+13x^2=-21+21 \\
\Leftrightarrow 7x^2 = 0 \\
\Leftrightarrow x^2 = \frac{0}{7}\\
\Leftrightarrow x = 0 \\
V = \Big\{ 0 \Big\} \\ -----------------\)
- \(2x^2-34=3x^2+2 \\ \Leftrightarrow 2x^2-3x^2=2+34 \\
\Leftrightarrow -x^2 = 36 \\
\Leftrightarrow x^2 = \frac{36}{-1} < 0 \\
V = \varnothing \\ -----------------\)
- \(5x^2+320=0 \\
\Leftrightarrow 5x^2 = -320 \\
\Leftrightarrow x^2 = \frac{-320}{5} < 0 \\
V = \varnothing \\ -----------------\)
- \(5(-10x^2+5)=-(44x^2-175) \\ \Leftrightarrow -50x^2+25=-44x^2+175 \\
\Leftrightarrow -50x^2+44x^2=175-25 \\
\Leftrightarrow -6x^2 = 150 \\
\Leftrightarrow x^2 = \frac{150}{-6} < 0 \\
V = \varnothing \\ -----------------\)
- \(-2x^2-392=0 \\
\Leftrightarrow -2x^2 = 392 \\
\Leftrightarrow x^2 = \frac{392}{-2} < 0 \\
V = \varnothing \\ -----------------\)
- \(-7x^2-10=-8x^2-9 \\ \Leftrightarrow -7x^2+8x^2=-9+10 \\
\Leftrightarrow x^2 = 1 \\
\Leftrightarrow x^2 = \frac{1}{1}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)
- \(-3(-9x^2-4)=-(-35x^2+500) \\ \Leftrightarrow 27x^2+12=35x^2-500 \\
\Leftrightarrow 27x^2-35x^2=-500-12 \\
\Leftrightarrow -8x^2 = -512 \\
\Leftrightarrow x^2 = \frac{-512}{-8}=64 \\
\Leftrightarrow x = 8 \vee x = -8 \\
V = \Big\{-8, 8 \Big\} \\ -----------------\)
- \(-2(10x^2+6)=-(25x^2+7) \\ \Leftrightarrow -20x^2-12=-25x^2-7 \\
\Leftrightarrow -20x^2+25x^2=-7+12 \\
\Leftrightarrow 5x^2 = 5 \\
\Leftrightarrow x^2 = \frac{5}{5}=1 \\
\Leftrightarrow x = 1 \vee x = -1 \\
V = \Big\{-1, 1 \Big\} \\ -----------------\)