Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-8x^2-159=-10x^2+3\)
2. \(-2(-7x^2+8)=-(-20x^2-80)\)
3. \(2x^2+24=10x^2-8\)
4. \(5(2x^2+10)=-(-2x^2-42)\)
5. \(2x^2-50=0\)
6. \(7x^2-112=0\)
7. \(-12x^2-293=-4x^2-5\)
8. \(5(9x^2-3)=-(-52x^2+862)\)
9. \(3(9x^2-9)=-(-29x^2+27)\)
10. \(12x^2+1178=5x^2-5\)
11. \(-2x^2-18=0\)
12. \(-4(2x^2+6)=-(15x^2-39)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-8x^2-159=-10x^2+3 \\ \Leftrightarrow -8x^2+10x^2=3+159 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
2. \(-2(-7x^2+8)=-(-20x^2-80) \\ \Leftrightarrow 14x^2-16=20x^2+80 \\ \Leftrightarrow 14x^2-20x^2=80+16 \\ \Leftrightarrow -6x^2 = 96 \\ \Leftrightarrow x^2 = \frac{96}{-6} < 0 \\ V = \varnothing \\ -----------------\)
3. \(2x^2+24=10x^2-8 \\ \Leftrightarrow 2x^2-10x^2=-8-24 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
4. \(5(2x^2+10)=-(-2x^2-42) \\ \Leftrightarrow 10x^2+50=2x^2+42 \\ \Leftrightarrow 10x^2-2x^2=42-50 \\ \Leftrightarrow 8x^2 = -8 \\ \Leftrightarrow x^2 = \frac{-8}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2x^2-50=0 \\ \Leftrightarrow 2x^2 = 50 \\ \Leftrightarrow x^2 = \frac{50}{2}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
6. \(7x^2-112=0 \\ \Leftrightarrow 7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
7. \(-12x^2-293=-4x^2-5 \\ \Leftrightarrow -12x^2+4x^2=-5+293 \\ \Leftrightarrow -8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{-8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(5(9x^2-3)=-(-52x^2+862) \\ \Leftrightarrow 45x^2-15=52x^2-862 \\ \Leftrightarrow 45x^2-52x^2=-862+15 \\ \Leftrightarrow -7x^2 = -847 \\ \Leftrightarrow x^2 = \frac{-847}{-7}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(3(9x^2-9)=-(-29x^2+27) \\ \Leftrightarrow 27x^2-27=29x^2-27 \\ \Leftrightarrow 27x^2-29x^2=-27+27 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(12x^2+1178=5x^2-5 \\ \Leftrightarrow 12x^2-5x^2=-5-1178 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-2x^2-18=0 \\ \Leftrightarrow -2x^2 = 18 \\ \Leftrightarrow x^2 = \frac{18}{-2} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4(2x^2+6)=-(15x^2-39) \\ \Leftrightarrow -8x^2-24=-15x^2+39 \\ \Leftrightarrow -8x^2+15x^2=39+24 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)