Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(-3x^2+285=3x^2-9\)
2. \(-x^2+121=0\)
3. \(7x^2-1183=0\)
4. \(-x^2+169=0\)
5. \(-11x^2+28=-9x^2-4\)
6. \(-x^2-81=0\)
7. \(-4(-3x^2+4)=-(-19x^2+1199)\)
8. \(x^2-144=0\)
9. \(12x^2-65=5x^2-2\)
10. \(3(6x^2-2)=-(-13x^2+186)\)
11. \(-3x^2-108=0\)
12. \(3(-7x^2+8)=-(26x^2-69)\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(-3x^2+285=3x^2-9 \\ \Leftrightarrow -3x^2-3x^2=-9-285 \\ \Leftrightarrow -6x^2 = -294 \\ \Leftrightarrow x^2 = \frac{-294}{-6}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
2. \(-x^2+121=0 \\ \Leftrightarrow -x^2 = -121 \\ \Leftrightarrow x^2 = \frac{-121}{-1}=121 \\ \Leftrightarrow x = 11 \vee x = -11 \\ V = \Big\{-11, 11 \Big\} \\ -----------------\)
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. \(-x^2+169=0 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
5. \(-11x^2+28=-9x^2-4 \\ \Leftrightarrow -11x^2+9x^2=-4-28 \\ \Leftrightarrow -2x^2 = -32 \\ \Leftrightarrow x^2 = \frac{-32}{-2}=16 \\ \Leftrightarrow x = 4 \vee x = -4 \\ V = \Big\{-4, 4 \Big\} \\ -----------------\)
6. \(-x^2-81=0 \\ \Leftrightarrow -x^2 = 81 \\ \Leftrightarrow x^2 = \frac{81}{-1} < 0 \\ V = \varnothing \\ -----------------\)
7. \(-4(-3x^2+4)=-(-19x^2+1199) \\ \Leftrightarrow 12x^2-16=19x^2-1199 \\ \Leftrightarrow 12x^2-19x^2=-1199+16 \\ \Leftrightarrow -7x^2 = -1183 \\ \Leftrightarrow x^2 = \frac{-1183}{-7}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(x^2-144=0 \\ \Leftrightarrow x^2 = 144 \\ \Leftrightarrow x^2 = \frac{144}{1}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
9. \(12x^2-65=5x^2-2 \\ \Leftrightarrow 12x^2-5x^2=-2+65 \\ \Leftrightarrow 7x^2 = 63 \\ \Leftrightarrow x^2 = \frac{63}{7}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)
10. \(3(6x^2-2)=-(-13x^2+186) \\ \Leftrightarrow 18x^2-6=13x^2-186 \\ \Leftrightarrow 18x^2-13x^2=-186+6 \\ \Leftrightarrow 5x^2 = -180 \\ \Leftrightarrow x^2 = \frac{-180}{5} < 0 \\ V = \varnothing \\ -----------------\)
11. \(-3x^2-108=0 \\ \Leftrightarrow -3x^2 = 108 \\ \Leftrightarrow x^2 = \frac{108}{-3} < 0 \\ V = \varnothing \\ -----------------\)
12. \(3(-7x^2+8)=-(26x^2-69) \\ \Leftrightarrow -21x^2+24=-26x^2+69 \\ \Leftrightarrow -21x^2+26x^2=69-24 \\ \Leftrightarrow 5x^2 = 45 \\ \Leftrightarrow x^2 = \frac{45}{5}=9 \\ \Leftrightarrow x = 3 \vee x = -3 \\ V = \Big\{-3, 3 \Big\} \\ -----------------\)