Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-5(3x^2-9)=-(13x^2-45)\)
2. \(5(9x^2-5)=-(-42x^2-407)\)
3. \(-4x^2+324=-9x^2+4\)
4. \(5(3x^2+6)=-(-23x^2-230)\)
5. \(2(5x^2+7)=-(-4x^2-110)\)
6. \(-3(10x^2+10)=-(31x^2+21)\)
7. \(-13x^2+93=-7x^2-3\)
8. \(2(9x^2-7)=-(-11x^2+1589)\)
9. \(-3(10x^2+5)=-(22x^2+215)\)
10. \(3x^2-47=2x^2+2\)
11. \(2(-2x^2-3)=-(-3x^2+181)\)
12. \(5(-8x^2-7)=-(46x^2-349)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-5(3x^2-9)=-(13x^2-45) \\ \Leftrightarrow -15x^2+45=-13x^2+45 \\ \Leftrightarrow -15x^2+13x^2=45-45 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(5(9x^2-5)=-(-42x^2-407) \\ \Leftrightarrow 45x^2-25=42x^2+407 \\ \Leftrightarrow 45x^2-42x^2=407+25 \\ \Leftrightarrow 3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{3}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(-4x^2+324=-9x^2+4 \\ \Leftrightarrow -4x^2+9x^2=4-324 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(3x^2+6)=-(-23x^2-230) \\ \Leftrightarrow 15x^2+30=23x^2+230 \\ \Leftrightarrow 15x^2-23x^2=230-30 \\ \Leftrightarrow -8x^2 = 200 \\ \Leftrightarrow x^2 = \frac{200}{-8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2(5x^2+7)=-(-4x^2-110) \\ \Leftrightarrow 10x^2+14=4x^2+110 \\ \Leftrightarrow 10x^2-4x^2=110-14 \\ \Leftrightarrow 6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(-3(10x^2+10)=-(31x^2+21) \\ \Leftrightarrow -30x^2-30=-31x^2-21 \\ \Leftrightarrow -30x^2+31x^2=-21+30 \\ \Leftrightarrow x^2 = 9 \\ \Leftrightarrow x^2 = \frac{9}{1}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
7. \(-13x^2+93=-7x^2-3 \\ \Leftrightarrow -13x^2+7x^2=-3-93 \\ \Leftrightarrow -6x^2 = -96 \\ \Leftrightarrow x^2 = \frac{-96}{-6}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(2(9x^2-7)=-(-11x^2+1589) \\ \Leftrightarrow 18x^2-14=11x^2-1589 \\ \Leftrightarrow 18x^2-11x^2=-1589+14 \\ \Leftrightarrow 7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3(10x^2+5)=-(22x^2+215) \\ \Leftrightarrow -30x^2-15=-22x^2-215 \\ \Leftrightarrow -30x^2+22x^2=-215+15 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
10. \(3x^2-47=2x^2+2 \\ \Leftrightarrow 3x^2-2x^2=2+47 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
11. \(2(-2x^2-3)=-(-3x^2+181) \\ \Leftrightarrow -4x^2-6=3x^2-181 \\ \Leftrightarrow -4x^2-3x^2=-181+6 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(5(-8x^2-7)=-(46x^2-349) \\ \Leftrightarrow -40x^2-35=-46x^2+349 \\ \Leftrightarrow -40x^2+46x^2=349+35 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)