Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2-64=0\)
2. \(-2(4x^2+5)=-(10x^2-88)\)
3. \(-3(-2x^2-9)=-(-13x^2+1156)\)
4. \(-5(-4x^2+4)=-(-17x^2+452)\)
5. \(-7x^2+112=0\)
6. \(2(4x^2-3)=-(-3x^2+6)\)
7. \(8x^2+1568=0\)
8. \(10x^2-1179=3x^2+4\)
9. \(-4(-9x^2-6)=-(-31x^2-1004)\)
10. \(4(-9x^2-3)=-(44x^2-1140)\)
11. \(11x^2+1=6x^2-4\)
12. \(6x^2-384=0\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2-64=0 \\ \Leftrightarrow 4x^2 = 64 \\ \Leftrightarrow x^2 = \frac{64}{4}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
2. \(-2(4x^2+5)=-(10x^2-88) \\ \Leftrightarrow -8x^2-10=-10x^2+88 \\ \Leftrightarrow -8x^2+10x^2=88+10 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
3. \(-3(-2x^2-9)=-(-13x^2+1156) \\ \Leftrightarrow 6x^2+27=13x^2-1156 \\ \Leftrightarrow 6x^2-13x^2=-1156-27 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-5(-4x^2+4)=-(-17x^2+452) \\ \Leftrightarrow 20x^2-20=17x^2-452 \\ \Leftrightarrow 20x^2-17x^2=-452+20 \\ \Leftrightarrow 3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{3} < 0 \\ V = \varnothing \\ -----------------\)
5. \(-7x^2+112=0 \\ \Leftrightarrow -7x^2 = -112 \\ \Leftrightarrow x^2 = \frac{-112}{-7}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(2(4x^2-3)=-(-3x^2+6) \\ \Leftrightarrow 8x^2-6=3x^2-6 \\ \Leftrightarrow 8x^2-3x^2=-6+6 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(8x^2+1568=0 \\ \Leftrightarrow 8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{8} < 0 \\ V = \varnothing \\ -----------------\)
8. \(10x^2-1179=3x^2+4 \\ \Leftrightarrow 10x^2-3x^2=4+1179 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
9. \(-4(-9x^2-6)=-(-31x^2-1004) \\ \Leftrightarrow 36x^2+24=31x^2+1004 \\ \Leftrightarrow 36x^2-31x^2=1004-24 \\ \Leftrightarrow 5x^2 = 980 \\ \Leftrightarrow x^2 = \frac{980}{5}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
10. \(4(-9x^2-3)=-(44x^2-1140) \\ \Leftrightarrow -36x^2-12=-44x^2+1140 \\ \Leftrightarrow -36x^2+44x^2=1140+12 \\ \Leftrightarrow 8x^2 = 1152 \\ \Leftrightarrow x^2 = \frac{1152}{8}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
11. \(11x^2+1=6x^2-4 \\ \Leftrightarrow 11x^2-6x^2=-4-1 \\ \Leftrightarrow 5x^2 = -5 \\ \Leftrightarrow x^2 = \frac{-5}{5} < 0 \\ V = \varnothing \\ -----------------\)
12. \(6x^2-384=0 \\ \Leftrightarrow 6x^2 = 384 \\ \Leftrightarrow x^2 = \frac{384}{6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)