Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2+900=0\)
2. \(-4(7x^2-4)=-(34x^2-16)\)
3. \(8x^2-128=0\)
4. \(-5x^2+39=-3x^2+7\)
5. \(-4(-8x^2+10)=-(-35x^2-35)\)
6. \(2x^2-704=-5x^2-4\)
7. \(-15x^2-135=-7x^2-7\)
8. \(2(2x^2-8)=-(4x^2+304)\)
9. \(4x^2-36=0\)
10. \(3x^2-1178=10x^2+5\)
11. \(7x^2-112=0\)
12. \(-5(9x^2+7)=-(52x^2-413)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2+900=0 \\ \Leftrightarrow -4x^2 = -900 \\ \Leftrightarrow x^2 = \frac{-900}{-4}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
2. \(-4(7x^2-4)=-(34x^2-16) \\ \Leftrightarrow -28x^2+16=-34x^2+16 \\ \Leftrightarrow -28x^2+34x^2=16-16 \\ \Leftrightarrow 6x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{6}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(8x^2-128=0 \\ \Leftrightarrow 8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{8}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
4. \(-5x^2+39=-3x^2+7 \\ \Leftrightarrow -5x^2+3x^2=7-39 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
5. \(-4(-8x^2+10)=-(-35x^2-35) \\ \Leftrightarrow 32x^2-40=35x^2+35 \\ \Leftrightarrow 32x^2-35x^2=35+40 \\ \Leftrightarrow -3x^2 = 75 \\ \Leftrightarrow x^2 = \frac{75}{-3} < 0 \\ V = \varnothing \\ -----------------\)
6. \(2x^2-704=-5x^2-4 \\ \Leftrightarrow 2x^2+5x^2=-4+704 \\ \Leftrightarrow 7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
7. \(-15x^2-135=-7x^2-7 \\ \Leftrightarrow -15x^2+7x^2=-7+135 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(2(2x^2-8)=-(4x^2+304) \\ \Leftrightarrow 4x^2-16=-4x^2-304 \\ \Leftrightarrow 4x^2+4x^2=-304+16 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4x^2-36=0 \\ \Leftrightarrow 4x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(3x^2-1178=10x^2+5 \\ \Leftrightarrow 3x^2-10x^2=5+1178 \\ \Leftrightarrow -7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{-7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(7x^2-112=0 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(-5(9x^2+7)=-(52x^2-413) \\ \Leftrightarrow -45x^2-35=-52x^2+413 \\ \Leftrightarrow -45x^2+52x^2=413+35 \\ \Leftrightarrow 7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)