Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2(-5x^2-8)=-(-4x^2-232)\)
2. \(9x^2+228=10x^2+3\)
3. \(-4x^2-144=0\)
4. \(-10x^2+145=-4x^2-5\)
5. \(5(10x^2-8)=-(-47x^2-548)\)
6. \(5(4x^2+4)=-(-25x^2+0)\)
7. \(4(10x^2-4)=-(-35x^2+11)\)
8. \(-11x^2+48=-6x^2+3\)
9. \(-3x^2+588=0\)
10. \(4(-10x^2+10)=-(48x^2-40)\)
11. \(-3(-6x^2-6)=-(-23x^2-38)\)
12. \(3(6x^2-9)=-(-16x^2+25)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2(-5x^2-8)=-(-4x^2-232) \\ \Leftrightarrow 10x^2+16=4x^2+232 \\ \Leftrightarrow 10x^2-4x^2=232-16 \\ \Leftrightarrow 6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{6}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(9x^2+228=10x^2+3 \\ \Leftrightarrow 9x^2-10x^2=3-228 \\ \Leftrightarrow -x^2 = -225 \\ \Leftrightarrow x^2 = \frac{-225}{-1}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
3. \(-4x^2-144=0 \\ \Leftrightarrow -4x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{-4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-10x^2+145=-4x^2-5 \\ \Leftrightarrow -10x^2+4x^2=-5-145 \\ \Leftrightarrow -6x^2 = -150 \\ \Leftrightarrow x^2 = \frac{-150}{-6}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(5(10x^2-8)=-(-47x^2-548) \\ \Leftrightarrow 50x^2-40=47x^2+548 \\ \Leftrightarrow 50x^2-47x^2=548+40 \\ \Leftrightarrow 3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
6. \(5(4x^2+4)=-(-25x^2+0) \\ \Leftrightarrow 20x^2+20=25x^2+0 \\ \Leftrightarrow 20x^2-25x^2=0-20 \\ \Leftrightarrow -5x^2 = -20 \\ \Leftrightarrow x^2 = \frac{-20}{-5}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
7. \(4(10x^2-4)=-(-35x^2+11) \\ \Leftrightarrow 40x^2-16=35x^2-11 \\ \Leftrightarrow 40x^2-35x^2=-11+16 \\ \Leftrightarrow 5x^2 = 5 \\ \Leftrightarrow x^2 = \frac{5}{5}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
8. \(-11x^2+48=-6x^2+3 \\ \Leftrightarrow -11x^2+6x^2=3-48 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-3x^2+588=0 \\ \Leftrightarrow -3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{-3}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(4(-10x^2+10)=-(48x^2-40) \\ \Leftrightarrow -40x^2+40=-48x^2+40 \\ \Leftrightarrow -40x^2+48x^2=40-40 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(-3(-6x^2-6)=-(-23x^2-38) \\ \Leftrightarrow 18x^2+18=23x^2+38 \\ \Leftrightarrow 18x^2-23x^2=38-18 \\ \Leftrightarrow -5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{-5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(6x^2-9)=-(-16x^2+25) \\ \Leftrightarrow 18x^2-27=16x^2-25 \\ \Leftrightarrow 18x^2-16x^2=-25+27 \\ \Leftrightarrow 2x^2 = 2 \\ \Leftrightarrow x^2 = \frac{2}{2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)