Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(7x^2-10)=-(-20x^2+506)\)
2. \(-4(-8x^2+6)=-(-26x^2-462)\)
3. \(-8x^2-1800=0\)
4. \(-8x^2-7=-6x^2-5\)
5. \(x^2-310=6x^2+10\)
6. \(2x^2-128=0\)
7. \(-8x^2-32=0\)
8. \(5(3x^2-2)=-(-17x^2+172)\)
9. \(-2(10x^2-9)=-(18x^2+54)\)
10. \(5(-8x^2+2)=-(38x^2-60)\)
11. \(-x^2+150=-4x^2+3\)
12. \(4x^2-4=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(7x^2-10)=-(-20x^2+506) \\ \Leftrightarrow 14x^2-20=20x^2-506 \\ \Leftrightarrow 14x^2-20x^2=-506+20 \\ \Leftrightarrow -6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{-6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-4(-8x^2+6)=-(-26x^2-462) \\ \Leftrightarrow 32x^2-24=26x^2+462 \\ \Leftrightarrow 32x^2-26x^2=462+24 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
3. \(-8x^2-1800=0 \\ \Leftrightarrow -8x^2 = 1800 \\ \Leftrightarrow x^2 = \frac{1800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-8x^2-7=-6x^2-5 \\ \Leftrightarrow -8x^2+6x^2=-5+7 \\ \Leftrightarrow -2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{-2} < 0 \\ V = \varnothing \\ -----------------\)
5. \(x^2-310=6x^2+10 \\ \Leftrightarrow x^2-6x^2=10+310 \\ \Leftrightarrow -5x^2 = 320 \\ \Leftrightarrow x^2 = \frac{320}{-5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(2x^2-128=0 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(-8x^2-32=0 \\ \Leftrightarrow -8x^2 = 32 \\ \Leftrightarrow x^2 = \frac{32}{-8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(3x^2-2)=-(-17x^2+172) \\ \Leftrightarrow 15x^2-10=17x^2-172 \\ \Leftrightarrow 15x^2-17x^2=-172+10 \\ \Leftrightarrow -2x^2 = -162 \\ \Leftrightarrow x^2 = \frac{-162}{-2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
9. \(-2(10x^2-9)=-(18x^2+54) \\ \Leftrightarrow -20x^2+18=-18x^2-54 \\ \Leftrightarrow -20x^2+18x^2=-54-18 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
10. \(5(-8x^2+2)=-(38x^2-60) \\ \Leftrightarrow -40x^2+10=-38x^2+60 \\ \Leftrightarrow -40x^2+38x^2=60-10 \\ \Leftrightarrow -2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{-2} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-x^2+150=-4x^2+3 \\ \Leftrightarrow -x^2+4x^2=3-150 \\ \Leftrightarrow 3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4x^2-4=0 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)