Onvolledige VKV (b=0)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

1. \(4(7x^2+5)=-(-25x^2+172)\)
2. \(-7x^2+0=0\)
3. \(-x^2+196=0\)
4. \(3x^2+10=7x^2+6\)
5. \(7x^2-7=9x^2-7\)
6. \(-5(-3x^2-4)=-(-13x^2-308)\)
7. \(2x^2+161=3x^2-8\)
8. \(-7x^2+175=0\)
9. \(-4x^2-324=0\)
10. \(-8x^2+1800=0\)
11. \(7x^2-343=0\)
12. \(11x^2+427=8x^2-5\)

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Los de vierkantsvergelijking op zonder de discriminant te gebruiken

Verbetersleutel

1. \(4(7x^2+5)=-(-25x^2+172) \\ \Leftrightarrow 28x^2+20=25x^2-172 \\ \Leftrightarrow 28x^2-25x^2=-172-20 \\ \Leftrightarrow 3x^2 = -192 \\ \Leftrightarrow x^2 = \frac{-192}{3} < 0 \\ V = \varnothing \\ -----------------\)
2. \(-7x^2+0=0 \\ \Leftrightarrow -7x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-7}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
3. \(-x^2+196=0 \\ \Leftrightarrow -x^2 = -196 \\ \Leftrightarrow x^2 = \frac{-196}{-1}=196 \\ \Leftrightarrow x = 14 \vee x = -14 \\ V = \Big\{-14, 14 \Big\} \\ -----------------\)
4. \(3x^2+10=7x^2+6 \\ \Leftrightarrow 3x^2-7x^2=6-10 \\ \Leftrightarrow -4x^2 = -4 \\ \Leftrightarrow x^2 = \frac{-4}{-4}=1 \\ \Leftrightarrow x = 1 \vee x = -1 \\ V = \Big\{-1, 1 \Big\} \\ -----------------\)
5. \(7x^2-7=9x^2-7 \\ \Leftrightarrow 7x^2-9x^2=-7+7 \\ \Leftrightarrow -2x^2 = 0 \\ \Leftrightarrow x^2 = \frac{0}{-2}\\ \Leftrightarrow x = 0 \\ V = \Big\{ 0 \Big\} \\ -----------------\)
6. \(-5(-3x^2-4)=-(-13x^2-308) \\ \Leftrightarrow 15x^2+20=13x^2+308 \\ \Leftrightarrow 15x^2-13x^2=308-20 \\ \Leftrightarrow 2x^2 = 288 \\ \Leftrightarrow x^2 = \frac{288}{2}=144 \\ \Leftrightarrow x = 12 \vee x = -12 \\ V = \Big\{-12, 12 \Big\} \\ -----------------\)
7. \(2x^2+161=3x^2-8 \\ \Leftrightarrow 2x^2-3x^2=-8-161 \\ \Leftrightarrow -x^2 = -169 \\ \Leftrightarrow x^2 = \frac{-169}{-1}=169 \\ \Leftrightarrow x = 13 \vee x = -13 \\ V = \Big\{-13, 13 \Big\} \\ -----------------\)
8. \(-7x^2+175=0 \\ \Leftrightarrow -7x^2 = -175 \\ \Leftrightarrow x^2 = \frac{-175}{-7}=25 \\ \Leftrightarrow x = 5 \vee x = -5 \\ V = \Big\{-5, 5 \Big\} \\ -----------------\)
9. \(-4x^2-324=0 \\ \Leftrightarrow -4x^2 = 324 \\ \Leftrightarrow x^2 = \frac{324}{-4} < 0 \\ V = \varnothing \\ -----------------\)
10. \(-8x^2+1800=0 \\ \Leftrightarrow -8x^2 = -1800 \\ \Leftrightarrow x^2 = \frac{-1800}{-8}=225 \\ \Leftrightarrow x = 15 \vee x = -15 \\ V = \Big\{-15, 15 \Big\} \\ -----------------\)
11. \(7x^2-343=0 \\ \Leftrightarrow 7x^2 = 343 \\ \Leftrightarrow x^2 = \frac{343}{7}=49 \\ \Leftrightarrow x = 7 \vee x = -7 \\ V = \Big\{-7, 7 \Big\} \\ -----------------\)
12. \(11x^2+427=8x^2-5 \\ \Leftrightarrow 11x^2-8x^2=-5-427 \\ \Leftrightarrow 3x^2 = -432 \\ \Leftrightarrow x^2 = \frac{-432}{3} < 0 \\ V = \varnothing \\ -----------------\)