Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2+32=0\)
2. \(4(-2x^2+3)=-(13x^2-12)\)
3. \(-2(-9x^2+5)=-(-12x^2-476)\)
4. \(8x^2+45=5x^2-3\)
5. \(4x^2+100=0\)
6. \(-5x^2-852=2x^2-5\)
7. \(-2x^2+128=0\)
8. \(-2(8x^2-4)=-(20x^2-792)\)
9. \(-3(10x^2+2)=-(25x^2+851)\)
10. \(15x^2-13=8x^2-6\)
11. \(3x^2-12=0\)
12. \(-8x^2+200=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2+32=0 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
2. \(4(-2x^2+3)=-(13x^2-12) \\ \Leftrightarrow -8x^2+12=-13x^2+12 \\ \Leftrightarrow -8x^2+13x^2=12-12 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-2(-9x^2+5)=-(-12x^2-476) \\ \Leftrightarrow 18x^2-10=12x^2+476 \\ \Leftrightarrow 18x^2-12x^2=476+10 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(8x^2+45=5x^2-3 \\ \Leftrightarrow 8x^2-5x^2=-3-45 \\ \Leftrightarrow 3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(4x^2+100=0 \\ \Leftrightarrow 4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{4} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5x^2-852=2x^2-5 \\ \Leftrightarrow -5x^2-2x^2=-5+852 \\ \Leftrightarrow -7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{-7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2x^2+128=0 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-2(8x^2-4)=-(20x^2-792) \\ \Leftrightarrow -16x^2+8=-20x^2+792 \\ \Leftrightarrow -16x^2+20x^2=792-8 \\ \Leftrightarrow 4x^2 = 784 \\ \Leftrightarrow x^2 = \frac{784}{4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
9. \(-3(10x^2+2)=-(25x^2+851) \\ \Leftrightarrow -30x^2-6=-25x^2-851 \\ \Leftrightarrow -30x^2+25x^2=-851+6 \\ \Leftrightarrow -5x^2 = -845 \\ \Leftrightarrow x^2 = \frac{-845}{-5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(15x^2-13=8x^2-6 \\ \Leftrightarrow 15x^2-8x^2=-6+13 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(3x^2-12=0 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-8x^2+200=0 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)