Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(6x^2-5)=-(-31x^2-24)\)
2. \(-2(-2x^2-7)=-(-7x^2-377)\)
3. \(-4(-2x^2-10)=-(-13x^2-45)\)
4. \(10x^2-1158=2x^2-6\)
5. \(-17x^2+1=-9x^2-7\)
6. \(-2(8x^2+6)=-(17x^2-4)\)
7. \(3(-9x^2+5)=-(34x^2-582)\)
8. \(2x^2-242=0\)
9. \(-2(5x^2-8)=-(3x^2+96)\)
10. \(2x^2+64=-6x^2-8\)
11. \(2x^2+377=8x^2-7\)
12. \(8x^2-1568=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(6x^2-5)=-(-31x^2-24) \\ \Leftrightarrow 30x^2-25=31x^2+24 \\ \Leftrightarrow 30x^2-31x^2=24+25 \\ \Leftrightarrow -x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2(-2x^2-7)=-(-7x^2-377) \\ \Leftrightarrow 4x^2+14=7x^2+377 \\ \Leftrightarrow 4x^2-7x^2=377-14 \\ \Leftrightarrow -3x^2 = 363 \\ \Leftrightarrow x^2 = \frac{363}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-4(-2x^2-10)=-(-13x^2-45) \\ \Leftrightarrow 8x^2+40=13x^2+45 \\ \Leftrightarrow 8x^2-13x^2=45-40 \\ \Leftrightarrow -5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{-5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(10x^2-1158=2x^2-6 \\ \Leftrightarrow 10x^2-2x^2=-6+1158 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
5. \(-17x^2+1=-9x^2-7 \\ \Leftrightarrow -17x^2+9x^2=-7-1 \\ \Leftrightarrow -8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{-8}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-2(8x^2+6)=-(17x^2-4) \\ \Leftrightarrow -16x^2-12=-17x^2+4 \\ \Leftrightarrow -16x^2+17x^2=4+12 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(3(-9x^2+5)=-(34x^2-582) \\ \Leftrightarrow -27x^2+15=-34x^2+582 \\ \Leftrightarrow -27x^2+34x^2=582-15 \\ \Leftrightarrow 7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{7}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(2x^2-242=0 \\ \Leftrightarrow 2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-2(5x^2-8)=-(3x^2+96) \\ \Leftrightarrow -10x^2+16=-3x^2-96 \\ \Leftrightarrow -10x^2+3x^2=-96-16 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
10. \(2x^2+64=-6x^2-8 \\ \Leftrightarrow 2x^2+6x^2=-8-64 \\ \Leftrightarrow 8x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(2x^2+377=8x^2-7 \\ \Leftrightarrow 2x^2-8x^2=-7-377 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
12. \(8x^2-1568=0 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)