Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-17x^2+1576=-9x^2+8\)
2. \(5(4x^2-7)=-(-15x^2-810)\)
3. \(-4x^2-154=-6x^2+8\)
4. \(14x^2-1123=9x^2+2\)
5. \(-5(5x^2+2)=-(32x^2-333)\)
6. \(-9x^2+438=-2x^2-10\)
7. \(5x^2+87=10x^2+7\)
8. \(-10x^2+246=-8x^2+4\)
9. \(-3(-10x^2-7)=-(-33x^2-69)\)
10. \(-11x^2+10=-8x^2+10\)
11. \(10x^2-5=3x^2-5\)
12. \(-6x^2-600=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-17x^2+1576=-9x^2+8 \\ \Leftrightarrow -17x^2+9x^2=8-1576 \\ \Leftrightarrow -8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{-8}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
2. \(5(4x^2-7)=-(-15x^2-810) \\ \Leftrightarrow 20x^2-35=15x^2+810 \\ \Leftrightarrow 20x^2-15x^2=810+35 \\ \Leftrightarrow 5x^2 = 845 \\ \Leftrightarrow x^2 = \frac{845}{5}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(-4x^2-154=-6x^2+8 \\ \Leftrightarrow -4x^2+6x^2=8+154 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(14x^2-1123=9x^2+2 \\ \Leftrightarrow 14x^2-9x^2=2+1123 \\ \Leftrightarrow 5x^2 = 1125 \\ \Leftrightarrow x^2 = \frac{1125}{5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
5. \(-5(5x^2+2)=-(32x^2-333) \\ \Leftrightarrow -25x^2-10=-32x^2+333 \\ \Leftrightarrow -25x^2+32x^2=333+10 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
6. \(-9x^2+438=-2x^2-10 \\ \Leftrightarrow -9x^2+2x^2=-10-438 \\ \Leftrightarrow -7x^2 = -448 \\ \Leftrightarrow x^2 = \frac{-448}{-7}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
7. \(5x^2+87=10x^2+7 \\ \Leftrightarrow 5x^2-10x^2=7-87 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
8. \(-10x^2+246=-8x^2+4 \\ \Leftrightarrow -10x^2+8x^2=4-246 \\ \Leftrightarrow -2x^2 = -242 \\ \Leftrightarrow x^2 = \frac{-242}{-2}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
9. \(-3(-10x^2-7)=-(-33x^2-69) \\ \Leftrightarrow 30x^2+21=33x^2+69 \\ \Leftrightarrow 30x^2-33x^2=69-21 \\ \Leftrightarrow -3x^2 = 48 \\ \Leftrightarrow x^2 = \frac{48}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-11x^2+10=-8x^2+10 \\ \Leftrightarrow -11x^2+8x^2=10-10 \\ \Leftrightarrow -3x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-3}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
11. \(10x^2-5=3x^2-5 \\ \Leftrightarrow 10x^2-3x^2=-5+5 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-6x^2-600=0 \\ \Leftrightarrow -6x^2 = 600 \\ \Leftrightarrow x^2 = \frac{600}{-6} < 0 \\ V = \varnothing \\ -----------------\)