Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(5(5x^2+9)=-(-24x^2-145)\)
2. \(13x^2+8=9x^2+8\)
3. \(-13x^2-843=-6x^2+4\)
4. \(3(-7x^2-10)=-(19x^2+30)\)
5. \(-8x^2-512=0\)
6. \(3x^2-3=0\)
7. \(3x^2+300=0\)
8. \(-10x^2-26=-3x^2+2\)
9. \(-5x^2+709=2x^2+9\)
10. \(10x^2-736=4x^2-10\)
11. \(-14x^2+85=-9x^2+5\)
12. \(5(3x^2+3)=-(-14x^2+106)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(5(5x^2+9)=-(-24x^2-145) \\ \Leftrightarrow 25x^2+45=24x^2+145 \\ \Leftrightarrow 25x^2-24x^2=145-45 \\ \Leftrightarrow x^2 = 100 \\ \Leftrightarrow x^2 = \frac{100}{1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
2. \(13x^2+8=9x^2+8 \\ \Leftrightarrow 13x^2-9x^2=8-8 \\ \Leftrightarrow 4x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{4}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-13x^2-843=-6x^2+4 \\ \Leftrightarrow -13x^2+6x^2=4+843 \\ \Leftrightarrow -7x^2 = 847 \\ \Leftrightarrow x^2 = \frac{847}{-7} < 0 \\ V = \varnothing \\ -----------------\)
4. \(3(-7x^2-10)=-(19x^2+30) \\ \Leftrightarrow -21x^2-30=-19x^2-30 \\ \Leftrightarrow -21x^2+19x^2=-30+30 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
5. \(-8x^2-512=0 \\ \Leftrightarrow -8x^2 = 512 \\ \Leftrightarrow x^2 = \frac{512}{-8} < 0 \\ V = \varnothing \\ -----------------\)
6. \(3x^2-3=0 \\ \Leftrightarrow 3x^2 = 3 \\ \Leftrightarrow x^2 = \frac{3}{3}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
7. \(3x^2+300=0 \\ \Leftrightarrow 3x^2 = -300 \\ \Leftrightarrow x^2 = \frac{-300}{3} < 0 \\ V = \varnothing \\ -----------------\)
8. \(-10x^2-26=-3x^2+2 \\ \Leftrightarrow -10x^2+3x^2=2+26 \\ \Leftrightarrow -7x^2 = 28 \\ \Leftrightarrow x^2 = \frac{28}{-7} < 0 \\ V = \varnothing \\ -----------------\)
9. \(-5x^2+709=2x^2+9 \\ \Leftrightarrow -5x^2-2x^2=9-709 \\ \Leftrightarrow -7x^2 = -700 \\ \Leftrightarrow x^2 = \frac{-700}{-7}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
10. \(10x^2-736=4x^2-10 \\ \Leftrightarrow 10x^2-4x^2=-10+736 \\ \Leftrightarrow 6x^2 = 726 \\ \Leftrightarrow x^2 = \frac{726}{6}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
11. \(-14x^2+85=-9x^2+5 \\ \Leftrightarrow -14x^2+9x^2=5-85 \\ \Leftrightarrow -5x^2 = -80 \\ \Leftrightarrow x^2 = \frac{-80}{-5}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
12. \(5(3x^2+3)=-(-14x^2+106) \\ \Leftrightarrow 15x^2+15=14x^2-106 \\ \Leftrightarrow 15x^2-14x^2=-106-15 \\ \Leftrightarrow x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{1} < 0 \\ V = \varnothing \\ -----------------\)