Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2x^2-9=3x^2+7\)
2. \(2(-2x^2+5)=-(x^2-202)\)
3. \(-5x^2-102=-9x^2-2\)
4. \(5x^2-143=8x^2+4\)
5. \(15x^2+46=9x^2-8\)
6. \(-3(2x^2-4)=-(10x^2-588)\)
7. \(3x^2+0=0\)
8. \(x^2+0=0\)
9. \(-4x^2+358=-7x^2-5\)
10. \(2(-3x^2-2)=-(4x^2+76)\)
11. \(-5(9x^2+5)=-(38x^2-542)\)
12. \(8x^2-187=7x^2+9\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2x^2-9=3x^2+7 \\ \Leftrightarrow 2x^2-3x^2=7+9 \\ \Leftrightarrow -x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{-1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(2(-2x^2+5)=-(x^2-202) \\ \Leftrightarrow -4x^2+10=-x^2+202 \\ \Leftrightarrow -4x^2+x^2=202-10 \\ \Leftrightarrow -3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{-3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-5x^2-102=-9x^2-2 \\ \Leftrightarrow -5x^2+9x^2=-2+102 \\ \Leftrightarrow 4x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{4}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
4. \(5x^2-143=8x^2+4 \\ \Leftrightarrow 5x^2-8x^2=4+143 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(15x^2+46=9x^2-8 \\ \Leftrightarrow 15x^2-9x^2=-8-46 \\ \Leftrightarrow 6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{6} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-3(2x^2-4)=-(10x^2-588) \\ \Leftrightarrow -6x^2+12=-10x^2+588 \\ \Leftrightarrow -6x^2+10x^2=588-12 \\ \Leftrightarrow 4x^2 = 576 \\ \Leftrightarrow x^2 = \frac{576}{4}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(3x^2+0=0 \\ \Leftrightarrow 3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(x^2+0=0 \\ \Leftrightarrow x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(-4x^2+358=-7x^2-5 \\ \Leftrightarrow -4x^2+7x^2=-5-358 \\ \Leftrightarrow 3x^2 = -363 \\ \Leftrightarrow x^2 = \frac{-363}{3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(2(-3x^2-2)=-(4x^2+76) \\ \Leftrightarrow -6x^2-4=-4x^2-76 \\ \Leftrightarrow -6x^2+4x^2=-76+4 \\ \Leftrightarrow -2x^2 = -72 \\ \Leftrightarrow x^2 = \frac{-72}{-2}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(-5(9x^2+5)=-(38x^2-542) \\ \Leftrightarrow -45x^2-25=-38x^2+542 \\ \Leftrightarrow -45x^2+38x^2=542+25 \\ \Leftrightarrow -7x^2 = 567 \\ \Leftrightarrow x^2 = \frac{567}{-7} < 0 \\ V = \varnothing \\ -----------------\)
12. \(8x^2-187=7x^2+9 \\ \Leftrightarrow 8x^2-7x^2=9+187 \\ \Leftrightarrow x^2 = 196 \\ \Leftrightarrow x^2 = \frac{196}{1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)