Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(2(-3x^2-8)=-(2x^2+52)\)
2. \(4x^2-676=0\)
3. \(17x^2-284=9x^2+4\)
4. \(4(-10x^2-5)=-(34x^2+404)\)
5. \(-4(-4x^2-5)=-(-9x^2-20)\)
6. \(-3x^2+3=0\)
7. \(2(-6x^2-9)=-(11x^2+118)\)
8. \(-8x^2-392=0\)
9. \(4(-2x^2+10)=-(11x^2-283)\)
10. \(5(-10x^2+5)=-(42x^2+1327)\)
11. \(4x^2+36=0\)
12. \(-4x^2+603=2x^2+3\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(2(-3x^2-8)=-(2x^2+52) \\ \Leftrightarrow -6x^2-16=-2x^2-52 \\ \Leftrightarrow -6x^2+2x^2=-52+16 \\ \Leftrightarrow -4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{-4}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
2. \(4x^2-676=0 \\ \Leftrightarrow 4x^2 = 676 \\ \Leftrightarrow x^2 = \frac{676}{4}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(17x^2-284=9x^2+4 \\ \Leftrightarrow 17x^2-9x^2=4+284 \\ \Leftrightarrow 8x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{8}=36 \\ \Leftrightarrow x = 6 \vee x = -6 \\ V = \Big\{-6, 6 \Big\} \\ -----------------\)
4. \(4(-10x^2-5)=-(34x^2+404) \\ \Leftrightarrow -40x^2-20=-34x^2-404 \\ \Leftrightarrow -40x^2+34x^2=-404+20 \\ \Leftrightarrow -6x^2 = -384 \\ \Leftrightarrow x^2 = \frac{-384}{-6}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(-4(-4x^2-5)=-(-9x^2-20) \\ \Leftrightarrow 16x^2+20=9x^2+20 \\ \Leftrightarrow 16x^2-9x^2=20-20 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
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. \(2(-6x^2-9)=-(11x^2+118) \\ \Leftrightarrow -12x^2-18=-11x^2-118 \\ \Leftrightarrow -12x^2+11x^2=-118+18 \\ \Leftrightarrow -x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{-1}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-8x^2-392=0 \\ \Leftrightarrow -8x^2 = 392 \\ \Leftrightarrow x^2 = \frac{392}{-8} < 0 \\ V = \varnothing \\ -----------------\)
9. \(4(-2x^2+10)=-(11x^2-283) \\ \Leftrightarrow -8x^2+40=-11x^2+283 \\ \Leftrightarrow -8x^2+11x^2=283-40 \\ \Leftrightarrow 3x^2 = 243 \\ \Leftrightarrow x^2 = \frac{243}{3}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
10. \(5(-10x^2+5)=-(42x^2+1327) \\ \Leftrightarrow -50x^2+25=-42x^2-1327 \\ \Leftrightarrow -50x^2+42x^2=-1327-25 \\ \Leftrightarrow -8x^2 = -1352 \\ \Leftrightarrow x^2 = \frac{-1352}{-8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
11. \(4x^2+36=0 \\ \Leftrightarrow 4x^2 = -36 \\ \Leftrightarrow x^2 = \frac{-36}{4} < 0 \\ V = \varnothing \\ -----------------\)
12. \(-4x^2+603=2x^2+3 \\ \Leftrightarrow -4x^2-2x^2=3-603 \\ \Leftrightarrow -6x^2 = -600 \\ \Leftrightarrow x^2 = \frac{-600}{-6}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)