Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2-261=7x^2-5\)
2. \(4x^2-255=-3x^2-3\)
3. \(-3x^2-507=0\)
4. \(5(-10x^2+6)=-(43x^2-478)\)
5. \(3x^2-411=-2x^2-6\)
6. \(-3x^2-6=-8x^2-6\)
7. \(-x^2-64=0\)
8. \(-2(-10x^2+8)=-(-19x^2-33)\)
9. \(-9x^2+1130=-4x^2+5\)
10. \(4(5x^2+9)=-(-13x^2+1147)\)
11. \(3x^2-315=7x^2+9\)
12. \(-5(-6x^2+5)=-(-37x^2+25)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2-261=7x^2-5 \\ \Leftrightarrow 11x^2-7x^2=-5+261 \\ \Leftrightarrow 4x^2 = 256 \\ \Leftrightarrow x^2 = \frac{256}{4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(4x^2-255=-3x^2-3 \\ \Leftrightarrow 4x^2+3x^2=-3+255 \\ \Leftrightarrow 7x^2 = 252 \\ \Leftrightarrow x^2 = \frac{252}{7}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
3. \(-3x^2-507=0 \\ \Leftrightarrow -3x^2 = 507 \\ \Leftrightarrow x^2 = \frac{507}{-3} < 0 \\ V = \varnothing \\ -----------------\)
4. \(5(-10x^2+6)=-(43x^2-478) \\ \Leftrightarrow -50x^2+30=-43x^2+478 \\ \Leftrightarrow -50x^2+43x^2=478-30 \\ \Leftrightarrow -7x^2 = 448 \\ \Leftrightarrow x^2 = \frac{448}{-7} < 0 \\ V = \varnothing \\ -----------------\)
5. \(3x^2-411=-2x^2-6 \\ \Leftrightarrow 3x^2+2x^2=-6+411 \\ \Leftrightarrow 5x^2 = 405 \\ \Leftrightarrow x^2 = \frac{405}{5}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
6. \(-3x^2-6=-8x^2-6 \\ \Leftrightarrow -3x^2+8x^2=-6+6 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-x^2-64=0 \\ \Leftrightarrow -x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{-1} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-2(-10x^2+8)=-(-19x^2-33) \\ \Leftrightarrow 20x^2-16=19x^2+33 \\ \Leftrightarrow 20x^2-19x^2=33+16 \\ \Leftrightarrow x^2 = 49 \\ \Leftrightarrow x^2 = \frac{49}{1}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
9. \(-9x^2+1130=-4x^2+5 \\ \Leftrightarrow -9x^2+4x^2=5-1130 \\ \Leftrightarrow -5x^2 = -1125 \\ \Leftrightarrow x^2 = \frac{-1125}{-5}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
10. \(4(5x^2+9)=-(-13x^2+1147) \\ \Leftrightarrow 20x^2+36=13x^2-1147 \\ \Leftrightarrow 20x^2-13x^2=-1147-36 \\ \Leftrightarrow 7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{7} < 0 \\ V = \varnothing \\ -----------------\)
11. \(3x^2-315=7x^2+9 \\ \Leftrightarrow 3x^2-7x^2=9+315 \\ \Leftrightarrow -4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{-4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-5(-6x^2+5)=-(-37x^2+25) \\ \Leftrightarrow 30x^2-25=37x^2-25 \\ \Leftrightarrow 30x^2-37x^2=-25+25 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)