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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2+51=-5x^2+3\)
2. \(4(10x^2-3)=-(-48x^2+300)\)
3. \(4x^2-64=0\)
4. \(-3x^2+8=-2x^2+8\)
5. \(-2x^2-242=0\)
6. \(-5x^2+720=0\)
7. \(-2x^2-162=0\)
8. \(-11x^2+696=-4x^2-4\)
9. \(-4(-3x^2+9)=-(-17x^2+36)\)
10. \(6x^2-1176=0\)
11. \(3(-4x^2+6)=-(15x^2-606)\)
12. \(4x^2-324=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2+51=-5x^2+3 \\ \Leftrightarrow -2x^2+5x^2=3-51 \\ \Leftrightarrow 3x^2 = -48 \\ \Leftrightarrow x^2 = \frac{-48}{3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(4(10x^2-3)=-(-48x^2+300) \\ \Leftrightarrow 40x^2-12=48x^2-300 \\ \Leftrightarrow 40x^2-48x^2=-300+12 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(4x^2-64=0 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-3x^2+8=-2x^2+8 \\ \Leftrightarrow -3x^2+2x^2=8-8 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-2x^2-242=0 \\ \Leftrightarrow -2x^2 = 242 \\ \Leftrightarrow x^2 = \frac{242}{-2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5x^2+720=0 \\ \Leftrightarrow -5x^2 = -720 \\ \Leftrightarrow x^2 = \frac{-720}{-5}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(-2x^2-162=0 \\ \Leftrightarrow -2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{-2} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-11x^2+696=-4x^2-4 \\ \Leftrightarrow -11x^2+4x^2=-4-696 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-4(-3x^2+9)=-(-17x^2+36) \\ \Leftrightarrow 12x^2-36=17x^2-36 \\ \Leftrightarrow 12x^2-17x^2=-36+36 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(6x^2-1176=0 \\ \Leftrightarrow 6x^2 = 1176 \\ \Leftrightarrow x^2 = \frac{1176}{6}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
11. \(3(-4x^2+6)=-(15x^2-606) \\ \Leftrightarrow -12x^2+18=-15x^2+606 \\ \Leftrightarrow -12x^2+15x^2=606-18 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(4x^2-324=0 \\ \Leftrightarrow 4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{4}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)