Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-13x^2+9=-10x^2+9\)
2. \(-2x^2-861=-8x^2+3\)
3. \(4(9x^2-5)=-(-31x^2+1000)\)
4. \(11x^2+483=5x^2-3\)
5. \(-3(8x^2+7)=-(20x^2+25)\)
6. \(-5(10x^2-5)=-(44x^2+1325)\)
7. \(6x^2+775=10x^2-9\)
8. \(4x^2-4=0\)
9. \(5x^2+6=6x^2+2\)
10. \(-2(-4x^2-5)=-(-13x^2-90)\)
11. \(-3(9x^2+4)=-(35x^2+44)\)
12. \(-2(-6x^2+9)=-(-20x^2-270)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-13x^2+9=-10x^2+9 \\ \Leftrightarrow -13x^2+10x^2=9-9 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
2. \(-2x^2-861=-8x^2+3 \\ \Leftrightarrow -2x^2+8x^2=3+861 \\ \Leftrightarrow 6x^2 = 864 \\ \Leftrightarrow x^2 = \frac{864}{6}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
3. \(4(9x^2-5)=-(-31x^2+1000) \\ \Leftrightarrow 36x^2-20=31x^2-1000 \\ \Leftrightarrow 36x^2-31x^2=-1000+20 \\ \Leftrightarrow 5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(11x^2+483=5x^2-3 \\ \Leftrightarrow 11x^2-5x^2=-3-483 \\ \Leftrightarrow 6x^2 = -486 \\ \Leftrightarrow x^2 = \frac{-486}{6} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-3(8x^2+7)=-(20x^2+25) \\ \Leftrightarrow -24x^2-21=-20x^2-25 \\ \Leftrightarrow -24x^2+20x^2=-25+21 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(-5(10x^2-5)=-(44x^2+1325) \\ \Leftrightarrow -50x^2+25=-44x^2-1325 \\ \Leftrightarrow -50x^2+44x^2=-1325-25 \\ \Leftrightarrow -6x^2 = -1350 \\ \Leftrightarrow x^2 = \frac{-1350}{-6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
7. \(6x^2+775=10x^2-9 \\ \Leftrightarrow 6x^2-10x^2=-9-775 \\ \Leftrightarrow -4x^2 = -784 \\ \Leftrightarrow x^2 = \frac{-784}{-4}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(4x^2-4=0 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
9. \(5x^2+6=6x^2+2 \\ \Leftrightarrow 5x^2-6x^2=2-6 \\ \Leftrightarrow -x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-1}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
10. \(-2(-4x^2-5)=-(-13x^2-90) \\ \Leftrightarrow 8x^2+10=13x^2+90 \\ \Leftrightarrow 8x^2-13x^2=90-10 \\ \Leftrightarrow -5x^2 = 80 \\ \Leftrightarrow x^2 = \frac{80}{-5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3(9x^2+4)=-(35x^2+44) \\ \Leftrightarrow -27x^2-12=-35x^2-44 \\ \Leftrightarrow -27x^2+35x^2=-44+12 \\ \Leftrightarrow 8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-2(-6x^2+9)=-(-20x^2-270) \\ \Leftrightarrow 12x^2-18=20x^2+270 \\ \Leftrightarrow 12x^2-20x^2=270+18 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)