Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5x^2+5=-6x^2-4\)
2. \(9x^2-304=6x^2-4\)
3. \(-13x^2+1803=-5x^2+3\)
4. \(5x^2+10=8x^2+7\)
5. \(x^2-185=-4x^2-5\)
6. \(3(6x^2+7)=-(-14x^2-697)\)
7. \(-3(-10x^2-5)=-(-34x^2-31)\)
8. \(-10x^2+153=-9x^2+9\)
9. \(5(8x^2-6)=-(-35x^2-950)\)
10. \(-3(-10x^2-10)=-(-29x^2+114)\)
11. \(4x^2+0=0\)
12. \(3x^2+1563=-5x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5x^2+5=-6x^2-4 \\ \Leftrightarrow -5x^2+6x^2=-4-5 \\ \Leftrightarrow x^2 = -9 \\ \Leftrightarrow x^2 = \frac{-9}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(9x^2-304=6x^2-4 \\ \Leftrightarrow 9x^2-6x^2=-4+304 \\ \Leftrightarrow 3x^2 = 300 \\ \Leftrightarrow x^2 = \frac{300}{3}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
3. \(-13x^2+1803=-5x^2+3 \\ \Leftrightarrow -13x^2+5x^2=3-1803 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(5x^2+10=8x^2+7 \\ \Leftrightarrow 5x^2-8x^2=7-10 \\ \Leftrightarrow -3x^2 = -3 \\ \Leftrightarrow x^2 = \frac{-3}{-3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(x^2-185=-4x^2-5 \\ \Leftrightarrow x^2+4x^2=-5+185 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
6. \(3(6x^2+7)=-(-14x^2-697) \\ \Leftrightarrow 18x^2+21=14x^2+697 \\ \Leftrightarrow 18x^2-14x^2=697-21 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
7. \(-3(-10x^2-5)=-(-34x^2-31) \\ \Leftrightarrow 30x^2+15=34x^2+31 \\ \Leftrightarrow 30x^2-34x^2=31-15 \\ \Leftrightarrow -4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-4} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-10x^2+153=-9x^2+9 \\ \Leftrightarrow -10x^2+9x^2=9-153 \\ \Leftrightarrow -x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{-1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(5(8x^2-6)=-(-35x^2-950) \\ \Leftrightarrow 40x^2-30=35x^2+950 \\ \Leftrightarrow 40x^2-35x^2=950+30 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(-3(-10x^2-10)=-(-29x^2+114) \\ \Leftrightarrow 30x^2+30=29x^2-114 \\ \Leftrightarrow 30x^2-29x^2=-114-30 \\ \Leftrightarrow x^2 = -144 \\ \Leftrightarrow x^2 = \frac{-144}{1} < 0 \\ V = \varnothing \\ -----------------\)
11. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(3x^2+1563=-5x^2-5 \\ \Leftrightarrow 3x^2+5x^2=-5-1563 \\ \Leftrightarrow 8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{8} < 0 \\ V = \varnothing \\ -----------------\)