Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+576=0\)
2. \(12x^2-54=10x^2-4\)
3. \(-3x^2-108=0\)
4. \(-2(2x^2+6)=-(9x^2-308)\)
5. \(3(-2x^2-7)=-(13x^2+21)\)
6. \(2x^2-34=3x^2+2\)
7. \(5x^2+320=0\)
8. \(5(-10x^2+5)=-(44x^2-175)\)
9. \(-2x^2-392=0\)
10. \(-7x^2-10=-8x^2-9\)
11. \(-3(-9x^2-4)=-(-35x^2+500)\)
12. \(-2(10x^2+6)=-(25x^2+7)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+576=0 \\ \Leftrightarrow 4x^2 = -576 \\ \Leftrightarrow x^2 = \frac{-576}{4} < 0 \\ V = \varnothing \\ -----------------\)
2. \(12x^2-54=10x^2-4 \\ \Leftrightarrow 12x^2-10x^2=-4+54 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
3. \(-3x^2-108=0 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(2x^2+6)=-(9x^2-308) \\ \Leftrightarrow -4x^2-12=-9x^2+308 \\ \Leftrightarrow -4x^2+9x^2=308+12 \\ \Leftrightarrow 5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(3(-2x^2-7)=-(13x^2+21) \\ \Leftrightarrow -6x^2-21=-13x^2-21 \\ \Leftrightarrow -6x^2+13x^2=-21+21 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(2x^2-34=3x^2+2 \\ \Leftrightarrow 2x^2-3x^2=2+34 \\ \Leftrightarrow -x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5x^2+320=0 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(-10x^2+5)=-(44x^2-175) \\ \Leftrightarrow -50x^2+25=-44x^2+175 \\ \Leftrightarrow -50x^2+44x^2=175-25 \\ \Leftrightarrow -6x^2 = 150 \\ \Leftrightarrow x^2 = \frac{150}{-6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-2x^2-392=0 \\ \Leftrightarrow -2x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-2} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-7x^2-10=-8x^2-9 \\ \Leftrightarrow -7x^2+8x^2=-9+10 \\ \Leftrightarrow x^2 = 1 \\ \Leftrightarrow x^2 = \frac{1}{1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(-3(-9x^2-4)=-(-35x^2+500) \\ \Leftrightarrow 27x^2+12=35x^2-500 \\ \Leftrightarrow 27x^2-35x^2=-500-12 \\ \Leftrightarrow -8x^2 = -512 \\ \Leftrightarrow x^2 = \frac{-512}{-8}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(-2(10x^2+6)=-(25x^2+7) \\ \Leftrightarrow -20x^2-12=-25x^2-7 \\ \Leftrightarrow -20x^2+25x^2=-7+12 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)