Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-x^2+36=0\)
2. \(x^2-3=3x^2-5\)
3. \(7x^2+448=0\)
4. \(-7x^2-700=0\)
5. \(2x^2-8=0\)
6. \(6x^2+600=0\)
7. \(3(9x^2-2)=-(-23x^2+6)\)
8. \(-2x^2-21=-3x^2+4\)
9. \(12x^2+1572=5x^2-3\)
10. \(10x^2-2=6x^2+2\)
11. \(5x^2-595=8x^2-7\)
12. \(5(-7x^2-6)=-(30x^2-470)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-x^2+36=0 \\ \Leftrightarrow -x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
2. \(x^2-3=3x^2-5 \\ \Leftrightarrow x^2-3x^2=-5+3 \\ \Leftrightarrow -2x^2 = -2 \\ \Leftrightarrow x^2 = \frac{-2}{-2}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
3. \(7x^2+448=0 \\ \Leftrightarrow 7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(-7x^2-700=0 \\ \Leftrightarrow -7x^2 = 700 \\ \Leftrightarrow x^2 = \frac{700}{-7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(2x^2-8=0 \\ \Leftrightarrow 2x^2 = 8 \\ \Leftrightarrow x^2 = \frac{8}{2}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
6. \(6x^2+600=0 \\ \Leftrightarrow 6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{6} < 0 \\ V = \varnothing \\ -----------------\)
7. \(3(9x^2-2)=-(-23x^2+6) \\ \Leftrightarrow 27x^2-6=23x^2-6 \\ \Leftrightarrow 27x^2-23x^2=-6+6 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
8. \(-2x^2-21=-3x^2+4 \\ \Leftrightarrow -2x^2+3x^2=4+21 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(12x^2+1572=5x^2-3 \\ \Leftrightarrow 12x^2-5x^2=-3-1572 \\ \Leftrightarrow 7x^2 = -1575 \\ \Leftrightarrow x^2 = \frac{-1575}{7} < 0 \\ V = \varnothing \\ -----------------\)
10. \(10x^2-2=6x^2+2 \\ \Leftrightarrow 10x^2-6x^2=2+2 \\ \Leftrightarrow 4x^2 = 4 \\ \Leftrightarrow x^2 = \frac{4}{4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
11. \(5x^2-595=8x^2-7 \\ \Leftrightarrow 5x^2-8x^2=-7+595 \\ \Leftrightarrow -3x^2 = 588 \\ \Leftrightarrow x^2 = \frac{588}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(5(-7x^2-6)=-(30x^2-470) \\ \Leftrightarrow -35x^2-30=-30x^2+470 \\ \Leftrightarrow -35x^2+30x^2=470+30 \\ \Leftrightarrow -5x^2 = 500 \\ \Leftrightarrow x^2 = \frac{500}{-5} < 0 \\ V = \varnothing \\ -----------------\)