Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(8x^2+288=0\)
2. \(-2x^2+32=0\)
3. \(5x^2-193=-3x^2+7\)
4. \(-10x^2+603=-4x^2+3\)
5. \(4x^2-64=0\)
6. \(3(-3x^2+2)=-(2x^2-34)\)
7. \(-7x^2+700=0\)
8. \(-6x^2-4=-10x^2-4\)
9. \(-3x^2-349=-10x^2-6\)
10. \(-12x^2+80=-10x^2+8\)
11. \(16x^2-594=10x^2+6\)
12. \(-3(-7x^2+2)=-(-15x^2-48)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(8x^2+288=0 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-2x^2+32=0 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
3. \(5x^2-193=-3x^2+7 \\ \Leftrightarrow 5x^2+3x^2=7+193 \\ \Leftrightarrow 8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(-10x^2+603=-4x^2+3 \\ \Leftrightarrow -10x^2+4x^2=3-603 \\ \Leftrightarrow -6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{-6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
5. \(4x^2-64=0 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(3(-3x^2+2)=-(2x^2-34) \\ \Leftrightarrow -9x^2+6=-2x^2+34 \\ \Leftrightarrow -9x^2+2x^2=34-6 \\ \Leftrightarrow -7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{-7} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-7x^2+700=0 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-6x^2-4=-10x^2-4 \\ \Leftrightarrow -6x^2+10x^2=-4+4 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-3x^2-349=-10x^2-6 \\ \Leftrightarrow -3x^2+10x^2=-6+349 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-12x^2+80=-10x^2+8 \\ \Leftrightarrow -12x^2+10x^2=8-80 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(16x^2-594=10x^2+6 \\ \Leftrightarrow 16x^2-10x^2=6+594 \\ \Leftrightarrow 6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
12. \(-3(-7x^2+2)=-(-15x^2-48) \\ \Leftrightarrow 21x^2-6=15x^2+48 \\ \Leftrightarrow 21x^2-15x^2=48+6 \\ \Leftrightarrow 6x^2 = 54 \\ \Leftrightarrow x^2 = \frac{54}{6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)