Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-4x^2+4)=-(10x^2-400)\)
2. \(-4(5x^2-2)=-(13x^2-855)\)
3. \(3x^2+48=0\)
4. \(-2(-9x^2-5)=-(-26x^2-2)\)
5. \(-5(-9x^2+9)=-(-47x^2-27)\)
6. \(x^2+225=0\)
7. \(8x^2+0=0\)
8. \(-x^2-908=3x^2-8\)
9. \(x^2-169=0\)
10. \(4x^2-1=3x^2+3\)
11. \(-11x^2+12=-9x^2+4\)
12. \(-3(3x^2-7)=-(3x^2-15)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-4x^2+4)=-(10x^2-400) \\ \Leftrightarrow -16x^2+16=-10x^2+400 \\ \Leftrightarrow -16x^2+10x^2=400-16 \\ \Leftrightarrow -6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{-6} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-4(5x^2-2)=-(13x^2-855) \\ \Leftrightarrow -20x^2+8=-13x^2+855 \\ \Leftrightarrow -20x^2+13x^2=855-8 \\ \Leftrightarrow -7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{-7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(3x^2+48=0 \\ \Leftrightarrow 3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(-9x^2-5)=-(-26x^2-2) \\ \Leftrightarrow 18x^2+10=26x^2+2 \\ \Leftrightarrow 18x^2-26x^2=2-10 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-5(-9x^2+9)=-(-47x^2-27) \\ \Leftrightarrow 45x^2-45=47x^2+27 \\ \Leftrightarrow 45x^2-47x^2=27+45 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(x^2+225=0 \\ \Leftrightarrow x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(8x^2+0=0 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-x^2-908=3x^2-8 \\ \Leftrightarrow -x^2-3x^2=-8+908 \\ \Leftrightarrow -4x^2 = 900 \\ \Leftrightarrow x^2 = \frac{900}{-4} < 0 \\ V = \varnothing \\ -----------------\)
9. \(x^2-169=0 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
10. \(4x^2-1=3x^2+3 \\ \Leftrightarrow 4x^2-3x^2=3+1 \\ \Leftrightarrow x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(-11x^2+12=-9x^2+4 \\ \Leftrightarrow -11x^2+9x^2=4-12 \\ \Leftrightarrow -2x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(-3(3x^2-7)=-(3x^2-15) \\ \Leftrightarrow -9x^2+21=-3x^2+15 \\ \Leftrightarrow -9x^2+3x^2=15-21 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)