Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-12x^2+69=-8x^2+5\)
2. \(-x^2+857=5x^2-7\)
3. \(2x^2-98=0\)
4. \(3x^2+75=0\)
5. \(6x^2+294=0\)
6. \(6x^2+6=0\)
7. \(-2(-4x^2+7)=-(-16x^2+14)\)
8. \(-7x^2+343=0\)
9. \(-5(-9x^2-7)=-(-52x^2+140)\)
10. \(4x^2+0=0\)
11. \(-7x^2-194=-8x^2+2\)
12. \(-5x^2+23=-8x^2-4\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-12x^2+69=-8x^2+5 \\ \Leftrightarrow -12x^2+8x^2=5-69 \\ \Leftrightarrow -4x^2 = -64 \\ \Leftrightarrow x^2 = \frac{-64}{-4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-x^2+857=5x^2-7 \\ \Leftrightarrow -x^2-5x^2=-7-857 \\ \Leftrightarrow -6x^2 = -864 \\ \Leftrightarrow x^2 = \frac{-864}{-6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(2x^2-98=0 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
4. \(3x^2+75=0 \\ \Leftrightarrow 3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(6x^2+294=0 \\ \Leftrightarrow 6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(6x^2+6=0 \\ \Leftrightarrow 6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2(-4x^2+7)=-(-16x^2+14) \\ \Leftrightarrow 8x^2-14=16x^2-14 \\ \Leftrightarrow 8x^2-16x^2=-14+14 \\ \Leftrightarrow -8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-7x^2+343=0 \\ \Leftrightarrow -7x^2 = -343 \\ \Leftrightarrow x^2 = \frac{-343}{-7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-5(-9x^2-7)=-(-52x^2+140) \\ \Leftrightarrow 45x^2+35=52x^2-140 \\ \Leftrightarrow 45x^2-52x^2=-140-35 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(4x^2+0=0 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-7x^2-194=-8x^2+2 \\ \Leftrightarrow -7x^2+8x^2=2+194 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(-5x^2+23=-8x^2-4 \\ \Leftrightarrow -5x^2+8x^2=-4-23 \\ \Leftrightarrow 3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{3} < 0 \\ V = \varnothing \\ -----------------\)