Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-2x^2-72=0\)
2. \(7x^2+1183=0\)
3. \(5(5x^2+7)=-(-24x^2-179)\)
4. \(x^2-282=-7x^2+6\)
5. \(2(8x^2+3)=-(-18x^2+282)\)
6. \(-5(6x^2+10)=-(27x^2-382)\)
7. \(-5(2x^2+6)=-(6x^2+30)\)
8. \(4(8x^2+2)=-(-28x^2-684)\)
9. \(-2(9x^2+4)=-(13x^2+988)\)
10. \(4x^2-400=0\)
11. \(-x^2+0=0\)
12. \(-3x^2-105=-6x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-2x^2-72=0 \\ \Leftrightarrow -2x^2 = 72 \\ \Leftrightarrow x^2 = \frac{72}{-2} < 0 \\ V = \varnothing \\ -----------------\)
2. \(7x^2+1183=0 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)
3. \(5(5x^2+7)=-(-24x^2-179) \\ \Leftrightarrow 25x^2+35=24x^2+179 \\ \Leftrightarrow 25x^2-24x^2=179-35 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
4. \(x^2-282=-7x^2+6 \\ \Leftrightarrow x^2+7x^2=6+282 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
5. \(2(8x^2+3)=-(-18x^2+282) \\ \Leftrightarrow 16x^2+6=18x^2-282 \\ \Leftrightarrow 16x^2-18x^2=-282-6 \\ \Leftrightarrow -2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{-2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
6. \(-5(6x^2+10)=-(27x^2-382) \\ \Leftrightarrow -30x^2-50=-27x^2+382 \\ \Leftrightarrow -30x^2+27x^2=382+50 \\ \Leftrightarrow -3x^2 = 432 \\ \Leftrightarrow x^2 = \frac{432}{-3} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-5(2x^2+6)=-(6x^2+30) \\ \Leftrightarrow -10x^2-30=-6x^2-30 \\ \Leftrightarrow -10x^2+6x^2=-30+30 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(4(8x^2+2)=-(-28x^2-684) \\ \Leftrightarrow 32x^2+8=28x^2+684 \\ \Leftrightarrow 32x^2-28x^2=684-8 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-2(9x^2+4)=-(13x^2+988) \\ \Leftrightarrow -18x^2-8=-13x^2-988 \\ \Leftrightarrow -18x^2+13x^2=-988+8 \\ \Leftrightarrow -5x^2 = -980 \\ \Leftrightarrow x^2 = \frac{-980}{-5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(4x^2-400=0 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
11. \(-x^2+0=0 \\ \Leftrightarrow -x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-1}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-3x^2-105=-6x^2+3 \\ \Leftrightarrow -3x^2+6x^2=3+105 \\ \Leftrightarrow 3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{3}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)