Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4x^2+197=7x^2+5\)
2. \(2x^2-1345=-6x^2+7\)
3. \(6x^2-1350=0\)
4. \(x^2-25=0\)
5. \(-2(-5x^2-6)=-(-9x^2-181)\)
6. \(-3(-5x^2+6)=-(-13x^2+306)\)
7. \(-14x^2+390=-10x^2-10\)
8. \(-3(-10x^2-2)=-(-22x^2-6)\)
9. \(11x^2+8=6x^2+8\)
10. \(3(-2x^2+4)=-(-x^2+51)\)
11. \(-3(-10x^2-5)=-(-28x^2-15)\)
12. \(5(8x^2+7)=-(-38x^2-133)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4x^2+197=7x^2+5 \\ \Leftrightarrow 4x^2-7x^2=5-197 \\ \Leftrightarrow -3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{-3}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
2. \(2x^2-1345=-6x^2+7 \\ \Leftrightarrow 2x^2+6x^2=7+1345 \\ \Leftrightarrow 8x^2 = 1352 \\ \Leftrightarrow x^2 = \frac{1352}{8}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
3. \(6x^2-1350=0 \\ \Leftrightarrow 6x^2 = 1350 \\ \Leftrightarrow x^2 = \frac{1350}{6}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
4. \(x^2-25=0 \\ \Leftrightarrow x^2 = 25 \\ \Leftrightarrow x^2 = \frac{25}{1}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
5. \(-2(-5x^2-6)=-(-9x^2-181) \\ \Leftrightarrow 10x^2+12=9x^2+181 \\ \Leftrightarrow 10x^2-9x^2=181-12 \\ \Leftrightarrow x^2 = 169 \\ \Leftrightarrow x^2 = \frac{169}{1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
6. \(-3(-5x^2+6)=-(-13x^2+306) \\ \Leftrightarrow 15x^2-18=13x^2-306 \\ \Leftrightarrow 15x^2-13x^2=-306+18 \\ \Leftrightarrow 2x^2 = -288 \\ \Leftrightarrow x^2 = \frac{-288}{2} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-14x^2+390=-10x^2-10 \\ \Leftrightarrow -14x^2+10x^2=-10-390 \\ \Leftrightarrow -4x^2 = -400 \\ \Leftrightarrow x^2 = \frac{-400}{-4}=100 \\ \Leftrightarrow x = 10 \vee x = -10 \\ V = \Big\{-10, 10 \Big\} \\ -----------------\)
8. \(-3(-10x^2-2)=-(-22x^2-6) \\ \Leftrightarrow 30x^2+6=22x^2+6 \\ \Leftrightarrow 30x^2-22x^2=6-6 \\ \Leftrightarrow 8x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{8}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(11x^2+8=6x^2+8 \\ \Leftrightarrow 11x^2-6x^2=8-8 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
10. \(3(-2x^2+4)=-(-x^2+51) \\ \Leftrightarrow -6x^2+12=x^2-51 \\ \Leftrightarrow -6x^2-x^2=-51-12 \\ \Leftrightarrow -7x^2 = -63 \\ \Leftrightarrow x^2 = \frac{-63}{-7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
11. \(-3(-10x^2-5)=-(-28x^2-15) \\ \Leftrightarrow 30x^2+15=28x^2+15 \\ \Leftrightarrow 30x^2-28x^2=15-15 \\ \Leftrightarrow 2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
12. \(5(8x^2+7)=-(-38x^2-133) \\ \Leftrightarrow 40x^2+35=38x^2+133 \\ \Leftrightarrow 40x^2-38x^2=133-35 \\ \Leftrightarrow 2x^2 = 98 \\ \Leftrightarrow x^2 = \frac{98}{2}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)