Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(11x^2-131=9x^2-3\)
2. \(-4(6x^2-6)=-(32x^2-416)\)
3. \(-3(2x^2+7)=-(10x^2+57)\)
4. \(8x^2+1152=0\)
5. \(5x^2-180=0\)
6. \(-5(2x^2-3)=-(14x^2-15)\)
7. \(-2(-3x^2-10)=-(x^2-1595)\)
8. \(-3x^2+173=-8x^2-7\)
9. \(2x^2-150=5x^2-3\)
10. \(7x^2-31=6x^2+5\)
11. \(4x^2+394=-2x^2+10\)
12. \(4x^2-400=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(11x^2-131=9x^2-3 \\ \Leftrightarrow 11x^2-9x^2=-3+131 \\ \Leftrightarrow 2x^2 = 128 \\ \Leftrightarrow x^2 = \frac{128}{2}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(-4(6x^2-6)=-(32x^2-416) \\ \Leftrightarrow -24x^2+24=-32x^2+416 \\ \Leftrightarrow -24x^2+32x^2=416-24 \\ \Leftrightarrow 8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{8}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-3(2x^2+7)=-(10x^2+57) \\ \Leftrightarrow -6x^2-21=-10x^2-57 \\ \Leftrightarrow -6x^2+10x^2=-57+21 \\ \Leftrightarrow 4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{4} < 0 \\ V = \varnothing \\ -----------------\)
4. \(8x^2+1152=0 \\ \Leftrightarrow 8x^2 = -1152 \\ \Leftrightarrow x^2 = \frac{-1152}{8} < 0 \\ V = \varnothing \\ -----------------\)
5. \(5x^2-180=0 \\ \Leftrightarrow 5x^2 = 180 \\ \Leftrightarrow x^2 = \frac{180}{5}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
6. \(-5(2x^2-3)=-(14x^2-15) \\ \Leftrightarrow -10x^2+15=-14x^2+15 \\ \Leftrightarrow -10x^2+14x^2=15-15 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-2(-3x^2-10)=-(x^2-1595) \\ \Leftrightarrow 6x^2+20=-x^2+1595 \\ \Leftrightarrow 6x^2+x^2=1595-20 \\ \Leftrightarrow 7x^2 = 1575 \\ \Leftrightarrow x^2 = \frac{1575}{7}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
8. \(-3x^2+173=-8x^2-7 \\ \Leftrightarrow -3x^2+8x^2=-7-173 \\ \Leftrightarrow 5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{5} < 0 \\ V = \varnothing \\ -----------------\)
9. \(2x^2-150=5x^2-3 \\ \Leftrightarrow 2x^2-5x^2=-3+150 \\ \Leftrightarrow -3x^2 = 147 \\ \Leftrightarrow x^2 = \frac{147}{-3} < 0 \\ V = \varnothing \\ -----------------\)
10. \(7x^2-31=6x^2+5 \\ \Leftrightarrow 7x^2-6x^2=5+31 \\ \Leftrightarrow x^2 = 36 \\ \Leftrightarrow x^2 = \frac{36}{1}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
11. \(4x^2+394=-2x^2+10 \\ \Leftrightarrow 4x^2+2x^2=10-394 \\ \Leftrightarrow 6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{6} < 0 \\ V = \varnothing \\ -----------------\)
12. \(4x^2-400=0 \\ \Leftrightarrow 4x^2 = 400 \\ \Leftrightarrow x^2 = \frac{400}{4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)