Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-17x^2-169=-10x^2+6\)
2. \(3x^2+588=0\)
3. \(-4(8x^2-7)=-(38x^2-514)\)
4. \(-2x^2-183=-5x^2+9\)
5. \(-4x^2+0=0\)
6. \(-5x^2-20=0\)
7. \(-7x^2+18=-6x^2-7\)
8. \(13x^2-26=9x^2-10\)
9. \(-14x^2+380=-8x^2-4\)
10. \(2(2x^2-2)=-(-11x^2-108)\)
11. \(-5x^2+2=-7x^2+2\)
12. \(-5(-4x^2-9)=-(-26x^2+9)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-17x^2-169=-10x^2+6 \\ \Leftrightarrow -17x^2+10x^2=6+169 \\ \Leftrightarrow -7x^2 = 175 \\ \Leftrightarrow x^2 = \frac{175}{-7} < 0 \\ V = \varnothing \\ -----------------\)
2. \(3x^2+588=0 \\ \Leftrightarrow 3x^2 = -588 \\ \Leftrightarrow x^2 = \frac{-588}{3} < 0 \\ V = \varnothing \\ -----------------\)
3. \(-4(8x^2-7)=-(38x^2-514) \\ \Leftrightarrow -32x^2+28=-38x^2+514 \\ \Leftrightarrow -32x^2+38x^2=514-28 \\ \Leftrightarrow 6x^2 = 486 \\ \Leftrightarrow x^2 = \frac{486}{6}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
4. \(-2x^2-183=-5x^2+9 \\ \Leftrightarrow -2x^2+5x^2=9+183 \\ \Leftrightarrow 3x^2 = 192 \\ \Leftrightarrow x^2 = \frac{192}{3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-4x^2+0=0 \\ \Leftrightarrow -4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-5x^2-20=0 \\ \Leftrightarrow -5x^2 = 20 \\ \Leftrightarrow x^2 = \frac{20}{-5} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-7x^2+18=-6x^2-7 \\ \Leftrightarrow -7x^2+6x^2=-7-18 \\ \Leftrightarrow -x^2 = -25 \\ \Leftrightarrow x^2 = \frac{-25}{-1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
8. \(13x^2-26=9x^2-10 \\ \Leftrightarrow 13x^2-9x^2=-10+26 \\ \Leftrightarrow 4x^2 = 16 \\ \Leftrightarrow x^2 = \frac{16}{4}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
9. \(-14x^2+380=-8x^2-4 \\ \Leftrightarrow -14x^2+8x^2=-4-380 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
10. \(2(2x^2-2)=-(-11x^2-108) \\ \Leftrightarrow 4x^2-4=11x^2+108 \\ \Leftrightarrow 4x^2-11x^2=108+4 \\ \Leftrightarrow -7x^2 = 112 \\ \Leftrightarrow x^2 = \frac{112}{-7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-5x^2+2=-7x^2+2 \\ \Leftrightarrow -5x^2+7x^2=2-2 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(-5(-4x^2-9)=-(-26x^2+9) \\ \Leftrightarrow 20x^2+45=26x^2-9 \\ \Leftrightarrow 20x^2-26x^2=-9-45 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)