Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-4x^2-300=-10x^2-6\)
2. \(3(-5x^2+5)=-(7x^2-1583)\)
3. \(-5(-3x^2-9)=-(-19x^2+439)\)
4. \(6x^2-639=-2x^2+9\)
5. \(-6x^2+150=0\)
6. \(-2(8x^2-6)=-(13x^2+576)\)
7. \(4(-8x^2+8)=-(34x^2-194)\)
8. \(3(-8x^2+5)=-(19x^2+305)\)
9. \(3x^2+149=6x^2+2\)
10. \(-3(2x^2-8)=-(7x^2-249)\)
11. \(11x^2-14=8x^2-2\)
12. \(4x^2-400=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-4x^2-300=-10x^2-6 \\ \Leftrightarrow -4x^2+10x^2=-6+300 \\ \Leftrightarrow 6x^2 = 294 \\ \Leftrightarrow x^2 = \frac{294}{6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(3(-5x^2+5)=-(7x^2-1583) \\ \Leftrightarrow -15x^2+15=-7x^2+1583 \\ \Leftrightarrow -15x^2+7x^2=1583-15 \\ \Leftrightarrow -8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{-8} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-5(-3x^2-9)=-(-19x^2+439) \\ \Leftrightarrow 15x^2+45=19x^2-439 \\ \Leftrightarrow 15x^2-19x^2=-439-45 \\ \Leftrightarrow -4x^2 = -484 \\ \Leftrightarrow x^2 = \frac{-484}{-4}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
4. \(6x^2-639=-2x^2+9 \\ \Leftrightarrow 6x^2+2x^2=9+639 \\ \Leftrightarrow 8x^2 = 648 \\ \Leftrightarrow x^2 = \frac{648}{8}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
5. \(-6x^2+150=0 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(-2(8x^2-6)=-(13x^2+576) \\ \Leftrightarrow -16x^2+12=-13x^2-576 \\ \Leftrightarrow -16x^2+13x^2=-576-12 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
7. \(4(-8x^2+8)=-(34x^2-194) \\ \Leftrightarrow -32x^2+32=-34x^2+194 \\ \Leftrightarrow -32x^2+34x^2=194-32 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
8. \(3(-8x^2+5)=-(19x^2+305) \\ \Leftrightarrow -24x^2+15=-19x^2-305 \\ \Leftrightarrow -24x^2+19x^2=-305-15 \\ \Leftrightarrow -5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{-5}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
9. \(3x^2+149=6x^2+2 \\ \Leftrightarrow 3x^2-6x^2=2-149 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
10. \(-3(2x^2-8)=-(7x^2-249) \\ \Leftrightarrow -6x^2+24=-7x^2+249 \\ \Leftrightarrow -6x^2+7x^2=249-24 \\ \Leftrightarrow x^2 = 225 \\ \Leftrightarrow x^2 = \frac{225}{1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(11x^2-14=8x^2-2 \\ \Leftrightarrow 11x^2-8x^2=-2+14 \\ \Leftrightarrow 3x^2 = 12 \\ \Leftrightarrow x^2 = \frac{12}{3}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
12. \(4x^2-400=0 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)