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a)
2x2−3=6−x2 ∣−6+x2
3x2−9=0 ∣:3
x2−3=0
(x−3)(x+3)=0
x−3=0 lub x+3=0
x=3 lub x=−3
b)
(31x+1)2=4
91x2+32x+1=4
91x2+32x−3=0 ∣⋅9
x2+6x−27=0
Δ=62−4⋅1⋅(−27)=36+108=144
x1=2−6−12=2−18=−9
x2=2−6+12=26=3
c)
(3x−2)2=(x+1)2
9x2−12x+4=x2+2x+1 ∣−x2−2x−1
8x2−14x+3=0
Δ=(−14)2−4⋅8⋅3=196−96=100
x1=2⋅814−10=164=41
x2=2⋅814+10=1624=46=23
d)
(2x−4)(2x+3)=1−11x
4x2+6x−8x−12=1−11x ∣−1+11x
4x2+9x−13=0
Δ=92−4⋅4⋅(−13)=81+208=289
x1=2⋅4−9−17=8−26=−413
x2=2⋅4−9+17=88=1
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