Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(-5x^2+3)=-(21x^2+109)\)
2. \(-15x^2+36=-10x^2-9\)
3. \(3(10x^2-7)=-(-25x^2+341)\)
4. \(-4(10x^2-7)=-(39x^2-27)\)
5. \(-3x^2+147=0\)
6. \(x^2+16=0\)
7. \(5x^2-1564=-3x^2+4\)
8. \(8x^2-800=0\)
9. \(-2x^2-837=-9x^2+10\)
10. \(8x^2+288=0\)
11. \(6x^2-486=0\)
12. \(-2(4x^2+8)=-(7x^2+16)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(-5x^2+3)=-(21x^2+109) \\ \Leftrightarrow -20x^2+12=-21x^2-109 \\ \Leftrightarrow -20x^2+21x^2=-109-12 \\ \Leftrightarrow x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{1} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-15x^2+36=-10x^2-9 \\ \Leftrightarrow -15x^2+10x^2=-9-36 \\ \Leftrightarrow -5x^2 = -45 \\ \Leftrightarrow x^2 = \frac{-45}{-5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
3. \(3(10x^2-7)=-(-25x^2+341) \\ \Leftrightarrow 30x^2-21=25x^2-341 \\ \Leftrightarrow 30x^2-25x^2=-341+21 \\ \Leftrightarrow 5x^2 = -320 \\ \Leftrightarrow x^2 = \frac{-320}{5} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-4(10x^2-7)=-(39x^2-27) \\ \Leftrightarrow -40x^2+28=-39x^2+27 \\ \Leftrightarrow -40x^2+39x^2=27-28 \\ \Leftrightarrow -x^2 = -1 \\ \Leftrightarrow x^2 = \frac{-1}{-1}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(-3x^2+147=0 \\ \Leftrightarrow -3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{-3}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(x^2+16=0 \\ \Leftrightarrow x^2 = -16 \\ \Leftrightarrow x^2 = \frac{-16}{1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(5x^2-1564=-3x^2+4 \\ \Leftrightarrow 5x^2+3x^2=4+1564 \\ \Leftrightarrow 8x^2 = 1568 \\ \Leftrightarrow x^2 = \frac{1568}{8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
8. \(8x^2-800=0 \\ \Leftrightarrow 8x^2 = 800 \\ \Leftrightarrow x^2 = \frac{800}{8}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
9. \(-2x^2-837=-9x^2+10 \\ \Leftrightarrow -2x^2+9x^2=10+837 \\ \Leftrightarrow 7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
10. \(8x^2+288=0 \\ \Leftrightarrow 8x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{8} < 0 \\ V = \varnothing \\ -----------------\)
11. \(6x^2-486=0 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
12. \(-2(4x^2+8)=-(7x^2+16) \\ \Leftrightarrow -8x^2-16=-7x^2-16 \\ \Leftrightarrow -8x^2+7x^2=-16+16 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)