Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(7x^2+145=4x^2-2\)
2. \(-8x^2+32=0\)
3. \(7x^2-1183=0\)
4. \(-4x^2+256=0\)
5. \(4(9x^2-9)=-(-42x^2+42)\)
6. \(x^2-5=-4x^2-5\)
7. \(-6x^2+54=0\)
8. \(7x^2+0=0\)
9. \(4(-3x^2+7)=-(16x^2+72)\)
10. \(-2(4x^2-3)=-(10x^2-168)\)
11. \(8x^2+1568=0\)
12. \(3(9x^2-5)=-(-35x^2+215)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(7x^2+145=4x^2-2 \\ \Leftrightarrow 7x^2-4x^2=-2-145 \\ \Leftrightarrow 3x^2 = -147 \\ \Leftrightarrow x^2 = \frac{-147}{3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-8x^2+32=0 \\ \Leftrightarrow -8x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-8}=4 \\ \Leftrightarrow x = 2 \vee x = -2 \\ V = \Big\{-2, 2 \Big\} \\ -----------------\)
3. \(7x^2-1183=0 \\ \Leftrightarrow 7x^2 = 1183 \\ \Leftrightarrow x^2 = \frac{1183}{7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
4. \(-4x^2+256=0 \\ \Leftrightarrow -4x^2 = -256 \\ \Leftrightarrow x^2 = \frac{-256}{-4}=64 \\ \Leftrightarrow x = 8 \vee x = -8 \\ V = \Big\{-8, 8 \Big\} \\ -----------------\)
5. \(4(9x^2-9)=-(-42x^2+42) \\ \Leftrightarrow 36x^2-36=42x^2-42 \\ \Leftrightarrow 36x^2-42x^2=-42+36 \\ \Leftrightarrow -6x^2 = -6 \\ \Leftrightarrow x^2 = \frac{-6}{-6}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
6. \(x^2-5=-4x^2-5 \\ \Leftrightarrow x^2+4x^2=-5+5 \\ \Leftrightarrow 5x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{5}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
7. \(-6x^2+54=0 \\ \Leftrightarrow -6x^2 = -54 \\ \Leftrightarrow x^2 = \frac{-54}{-6}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
8. \(7x^2+0=0 \\ \Leftrightarrow 7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
9. \(4(-3x^2+7)=-(16x^2+72) \\ \Leftrightarrow -12x^2+28=-16x^2-72 \\ \Leftrightarrow -12x^2+16x^2=-72-28 \\ \Leftrightarrow 4x^2 = -100 \\ \Leftrightarrow x^2 = \frac{-100}{4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-2(4x^2-3)=-(10x^2-168) \\ \Leftrightarrow -8x^2+6=-10x^2+168 \\ \Leftrightarrow -8x^2+10x^2=168-6 \\ \Leftrightarrow 2x^2 = 162 \\ \Leftrightarrow x^2 = \frac{162}{2}=81 \\ \Leftrightarrow x = 9 \vee x = -9 \\ V = \Big\{-9, 9 \Big\} \\ -----------------\)
11. \(8x^2+1568=0 \\ \Leftrightarrow 8x^2 = -1568 \\ \Leftrightarrow x^2 = \frac{-1568}{8} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(9x^2-5)=-(-35x^2+215) \\ \Leftrightarrow 27x^2-15=35x^2-215 \\ \Leftrightarrow 27x^2-35x^2=-215+15 \\ \Leftrightarrow -8x^2 = -200 \\ \Leftrightarrow x^2 = \frac{-200}{-8}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)