Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2-700=0\)
2. \(6x^2+782=10x^2-2\)
3. \(2x^2+242=0\)
4. \(-2(-10x^2+8)=-(-28x^2-784)\)
5. \(-5(5x^2-9)=-(27x^2+5)\)
6. \(3(2x^2-9)=-(-2x^2-169)\)
7. \(-4(4x^2+4)=-(14x^2+16)\)
8. \(x^2-225=0\)
9. \(-x^2+709=-8x^2+9\)
10. \(-3(-5x^2+9)=-(-19x^2+223)\)
11. \(-4(-7x^2-5)=-(-31x^2+55)\)
12. \(-3x^2-186=-6x^2+6\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2-700=0 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(6x^2+782=10x^2-2 \\ \Leftrightarrow 6x^2-10x^2=-2-782 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
3. \(2x^2+242=0 \\ \Leftrightarrow 2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{2} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-2(-10x^2+8)=-(-28x^2-784) \\ \Leftrightarrow 20x^2-16=28x^2+784 \\ \Leftrightarrow 20x^2-28x^2=784+16 \\ \Leftrightarrow -8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-5(5x^2-9)=-(27x^2+5) \\ \Leftrightarrow -25x^2+45=-27x^2-5 \\ \Leftrightarrow -25x^2+27x^2=-5-45 \\ \Leftrightarrow 2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{2} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3(2x^2-9)=-(-2x^2-169) \\ \Leftrightarrow 6x^2-27=2x^2+169 \\ \Leftrightarrow 6x^2-2x^2=169+27 \\ \Leftrightarrow 4x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-4(4x^2+4)=-(14x^2+16) \\ \Leftrightarrow -16x^2-16=-14x^2-16 \\ \Leftrightarrow -16x^2+14x^2=-16+16 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(x^2-225=0 \\ \Leftrightarrow x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(-x^2+709=-8x^2+9 \\ \Leftrightarrow -x^2+8x^2=9-709 \\ \Leftrightarrow 7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-3(-5x^2+9)=-(-19x^2+223) \\ \Leftrightarrow 15x^2-27=19x^2-223 \\ \Leftrightarrow 15x^2-19x^2=-223+27 \\ \Leftrightarrow -4x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-4}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(-4(-7x^2-5)=-(-31x^2+55) \\ \Leftrightarrow 28x^2+20=31x^2-55 \\ \Leftrightarrow 28x^2-31x^2=-55-20 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-3x^2-186=-6x^2+6 \\ \Leftrightarrow -3x^2+6x^2=6+186 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)