Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5x^2-134=-3x^2-6\)
2. \(-5(-4x^2-5)=-(-17x^2-172)\)
3. \(8x^2+128=0\)
4. \(-4(5x^2-5)=-(22x^2-28)\)
5. \(-2x^2+288=0\)
6. \(-4(2x^2-10)=-(7x^2-265)\)
7. \(x^2-16=0\)
8. \(4(-9x^2-5)=-(32x^2+920)\)
9. \(3x^2-384=-5x^2+8\)
10. \(8x^2+120=10x^2-8\)
11. \(-4x^2+484=0\)
12. \(3(-9x^2-5)=-(23x^2+799)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5x^2-134=-3x^2-6 \\ \Leftrightarrow 5x^2+3x^2=-6+134 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-5(-4x^2-5)=-(-17x^2-172) \\ \Leftrightarrow 20x^2+25=17x^2+172 \\ \Leftrightarrow 20x^2-17x^2=172-25 \\ \Leftrightarrow 3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(8x^2+128=0 \\ \Leftrightarrow 8x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4(5x^2-5)=-(22x^2-28) \\ \Leftrightarrow -20x^2+20=-22x^2+28 \\ \Leftrightarrow -20x^2+22x^2=28-20 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
5. \(-2x^2+288=0 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(-4(2x^2-10)=-(7x^2-265) \\ \Leftrightarrow -8x^2+40=-7x^2+265 \\ \Leftrightarrow -8x^2+7x^2=265-40 \\ \Leftrightarrow -x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(x^2-16=0 \\ \Leftrightarrow x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{1}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(4(-9x^2-5)=-(32x^2+920) \\ \Leftrightarrow -36x^2-20=-32x^2-920 \\ \Leftrightarrow -36x^2+32x^2=-920+20 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
9. \(3x^2-384=-5x^2+8 \\ \Leftrightarrow 3x^2+5x^2=8+384 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(8x^2+120=10x^2-8 \\ \Leftrightarrow 8x^2-10x^2=-8-120 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
11. \(-4x^2+484=0 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
12. \(3(-9x^2-5)=-(23x^2+799) \\ \Leftrightarrow -27x^2-15=-23x^2-799 \\ \Leftrightarrow -27x^2+23x^2=-799+15 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)