Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2-792=3x^2+8\)
2. \(2(-2x^2-8)=-(0x^2+500)\)
3. \(3(-7x^2-8)=-(22x^2+24)\)
4. \(11x^2+387=3x^2-5\)
5. \(-3(-10x^2-5)=-(-38x^2-143)\)
6. \(-5(-8x^2+9)=-(-39x^2-36)\)
7. \(-x^2-144=0\)
8. \(-3x^2+44=-9x^2-10\)
9. \(-x^2-4=4x^2-4\)
10. \(7x^2-442=4x^2-10\)
11. \(2(-3x^2+2)=-(4x^2+46)\)
12. \(-4x^2+678=-8x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2-792=3x^2+8 \\ \Leftrightarrow -5x^2-3x^2=8+792 \\ \Leftrightarrow -8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2(-2x^2-8)=-(0x^2+500) \\ \Leftrightarrow -4x^2-16=0x^2-500 \\ \Leftrightarrow -4x^2+0x^2=-500+16 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(3(-7x^2-8)=-(22x^2+24) \\ \Leftrightarrow -21x^2-24=-22x^2-24 \\ \Leftrightarrow -21x^2+22x^2=-24+24 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
4. \(11x^2+387=3x^2-5 \\ \Leftrightarrow 11x^2-3x^2=-5-387 \\ \Leftrightarrow 8x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(-10x^2-5)=-(-38x^2-143) \\ \Leftrightarrow 30x^2+15=38x^2+143 \\ \Leftrightarrow 30x^2-38x^2=143-15 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-5(-8x^2+9)=-(-39x^2-36) \\ \Leftrightarrow 40x^2-45=39x^2+36 \\ \Leftrightarrow 40x^2-39x^2=36+45 \\ \Leftrightarrow x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{1}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
7. \(-x^2-144=0 \\ \Leftrightarrow -x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-3x^2+44=-9x^2-10 \\ \Leftrightarrow -3x^2+9x^2=-10-44 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-x^2-4=4x^2-4 \\ \Leftrightarrow -x^2-4x^2=-4+4 \\ \Leftrightarrow -5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(7x^2-442=4x^2-10 \\ \Leftrightarrow 7x^2-4x^2=-10+442 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(2(-3x^2+2)=-(4x^2+46) \\ \Leftrightarrow -6x^2+4=-4x^2-46 \\ \Leftrightarrow -6x^2+4x^2=-46-4 \\ \Leftrightarrow -2x^2 = -50 \\ \Leftrightarrow x^2 = \frac{-50}{-2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-4x^2+678=-8x^2+2 \\ \Leftrightarrow -4x^2+8x^2=2-678 \\ \Leftrightarrow 4x^2 = -676 \\ \Leftrightarrow x^2 = \frac{-676}{4} < 0 \\ V = \varnothing \\ -----------------\)