Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-10x^2+2)=-(18x^2-132)\)
2. \(-7x^2-96=-6x^2+4\)
3. \(5(6x^2+5)=-(-26x^2-29)\)
4. \(-3x^2+675=0\)
5. \(5x^2+320=0\)
6. \(-x^2+49=0\)
7. \(-6x^2-216=0\)
8. \(3(7x^2+8)=-(-18x^2-51)\)
9. \(-2x^2-119=6x^2+9\)
10. \(7x^2-28=0\)
11. \(-2x^2+392=0\)
12. \(-3(-10x^2-10)=-(-38x^2+258)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-10x^2+2)=-(18x^2-132) \\ \Leftrightarrow -20x^2+4=-18x^2+132 \\ \Leftrightarrow -20x^2+18x^2=132-4 \\ \Leftrightarrow -2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-7x^2-96=-6x^2+4 \\ \Leftrightarrow -7x^2+6x^2=4+96 \\ \Leftrightarrow -x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{-1} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5(6x^2+5)=-(-26x^2-29) \\ \Leftrightarrow 30x^2+25=26x^2+29 \\ \Leftrightarrow 30x^2-26x^2=29-25 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
4. \(-3x^2+675=0 \\ \Leftrightarrow -3x^2 = -675 \\ \Leftrightarrow x^2 = \frac{-675}{-3}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(5x^2+320=0 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
6. \(-x^2+49=0 \\ \Leftrightarrow -x^2 = -49 \\ \Leftrightarrow x^2 = \frac{-49}{-1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
7. \(-6x^2-216=0 \\ \Leftrightarrow -6x^2 = 216 \\ \Leftrightarrow x^2 = \frac{216}{-6} < 0 \\ V = \varnothing \\ -----------------\)
8. \(3(7x^2+8)=-(-18x^2-51) \\ \Leftrightarrow 21x^2+24=18x^2+51 \\ \Leftrightarrow 21x^2-18x^2=51-24 \\ \Leftrightarrow 3x^2 = 27 \\ \Leftrightarrow x^2 = \frac{27}{3}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
9. \(-2x^2-119=6x^2+9 \\ \Leftrightarrow -2x^2-6x^2=9+119 \\ \Leftrightarrow -8x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{-8} < 0 \\ V = \varnothing \\ -----------------\)
10. \(7x^2-28=0 \\ \Leftrightarrow 7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{7}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
11. \(-2x^2+392=0 \\ \Leftrightarrow -2x^2 = -392 \\ \Leftrightarrow x^2 = \frac{-392}{-2}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
12. \(-3(-10x^2-10)=-(-38x^2+258) \\ \Leftrightarrow 30x^2+30=38x^2-258 \\ \Leftrightarrow 30x^2-38x^2=-258-30 \\ \Leftrightarrow -8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)