Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-4x^2-8)=-(7x^2+212)\)
2. \(-6x^2+6=-8x^2+6\)
3. \(-4(9x^2+8)=-(31x^2+32)\)
4. \(-x^2+682=3x^2+6\)
5. \(7x^2+175=0\)
6. \(-4(5x^2-4)=-(12x^2-1168)\)
7. \(5(6x^2+6)=-(-22x^2-678)\)
8. \(5(8x^2-9)=-(-43x^2+33)\)
9. \(8x^2-200=0\)
10. \(3x^2-48=0\)
11. \(-2(3x^2+6)=-(x^2-8)\)
12. \(-3(-6x^2-4)=-(-13x^2-17)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-4x^2-8)=-(7x^2+212) \\ \Leftrightarrow -8x^2-16=-7x^2-212 \\ \Leftrightarrow -8x^2+7x^2=-212+16 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(-6x^2+6=-8x^2+6 \\ \Leftrightarrow -6x^2+8x^2=6-6 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-4(9x^2+8)=-(31x^2+32) \\ \Leftrightarrow -36x^2-32=-31x^2-32 \\ \Leftrightarrow -36x^2+31x^2=-32+32 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(-x^2+682=3x^2+6 \\ \Leftrightarrow -x^2-3x^2=6-682 \\ \Leftrightarrow -4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{-4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(7x^2+175=0 \\ \Leftrightarrow 7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{7} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-4(5x^2-4)=-(12x^2-1168) \\ \Leftrightarrow -20x^2+16=-12x^2+1168 \\ \Leftrightarrow -20x^2+12x^2=1168-16 \\ \Leftrightarrow -8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{-8} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5(6x^2+6)=-(-22x^2-678) \\ \Leftrightarrow 30x^2+30=22x^2+678 \\ \Leftrightarrow 30x^2-22x^2=678-30 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(5(8x^2-9)=-(-43x^2+33) \\ \Leftrightarrow 40x^2-45=43x^2-33 \\ \Leftrightarrow 40x^2-43x^2=-33+45 \\ \Leftrightarrow -3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(8x^2-200=0 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(3x^2-48=0 \\ \Leftrightarrow 3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{3}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
11. \(-2(3x^2+6)=-(x^2-8) \\ \Leftrightarrow -6x^2-12=-x^2+8 \\ \Leftrightarrow -6x^2+x^2=8+12 \\ \Leftrightarrow -5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{-5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-3(-6x^2-4)=-(-13x^2-17) \\ \Leftrightarrow 18x^2+12=13x^2+17 \\ \Leftrightarrow 18x^2-13x^2=17-12 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)