Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-800=0\)
2. \(6x^2-973=-2x^2-5\)
3. \(-7x^2+63=0\)
4. \(-3(-2x^2-9)=-(-9x^2+0)\)
5. \(-3x^2+164=-2x^2-5\)
6. \(2(-7x^2+4)=-(11x^2-11)\)
7. \(-2x^2+128=0\)
8. \(-4(-6x^2-8)=-(-27x^2-539)\)
9. \(-3(6x^2+7)=-(19x^2+37)\)
10. \(-2x^2-15=-9x^2-8\)
11. \(3(2x^2+3)=-(-9x^2+66)\)
12. \(-18x^2+202=-10x^2+2\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-800=0 \\ \Leftrightarrow -8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{-8} < 0 \\ V = \varnothing \\ -----------------\)
2. \(6x^2-973=-2x^2-5 \\ \Leftrightarrow 6x^2+2x^2=-5+973 \\ \Leftrightarrow 8x^2 = 968 \\ \Leftrightarrow x^2 = \frac{968}{8}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
3. \(-7x^2+63=0 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
4. \(-3(-2x^2-9)=-(-9x^2+0) \\ \Leftrightarrow 6x^2+27=9x^2+0 \\ \Leftrightarrow 6x^2-9x^2=0-27 \\ \Leftrightarrow -3x^2 = -27 \\ \Leftrightarrow x^2 = \frac{-27}{-3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
5. \(-3x^2+164=-2x^2-5 \\ \Leftrightarrow -3x^2+2x^2=-5-164 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(2(-7x^2+4)=-(11x^2-11) \\ \Leftrightarrow -14x^2+8=-11x^2+11 \\ \Leftrightarrow -14x^2+11x^2=11-8 \\ \Leftrightarrow -3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{-3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-2x^2+128=0 \\ \Leftrightarrow -2x^2 = -128 \\ \Leftrightarrow x^2 = \frac{-128}{-2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
8. \(-4(-6x^2-8)=-(-27x^2-539) \\ \Leftrightarrow 24x^2+32=27x^2+539 \\ \Leftrightarrow 24x^2-27x^2=539-32 \\ \Leftrightarrow -3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{-3} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-3(6x^2+7)=-(19x^2+37) \\ \Leftrightarrow -18x^2-21=-19x^2-37 \\ \Leftrightarrow -18x^2+19x^2=-37+21 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2x^2-15=-9x^2-8 \\ \Leftrightarrow -2x^2+9x^2=-8+15 \\ \Leftrightarrow 7x^2 = 7 \\ \Leftrightarrow x^2 = \frac{7}{7}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(3(2x^2+3)=-(-9x^2+66) \\ \Leftrightarrow 6x^2+9=9x^2-66 \\ \Leftrightarrow 6x^2-9x^2=-66-9 \\ \Leftrightarrow -3x^2 = -75 \\ \Leftrightarrow x^2 = \frac{-75}{-3}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
12. \(-18x^2+202=-10x^2+2 \\ \Leftrightarrow -18x^2+10x^2=2-202 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)