Вправа 383 алгебра Бевз гдз 7 клас

№ 383

а) (2x² – 3)(x – 3) = 2x(x – 3) + 6
2x³ – 6x² – 3x + 9 = 2x³ – 6x² + 6
–3x = 6 – 9
–3x = –3
x = 1;

б) (0,1 + х)(0,01 – 0,1x + х²) = 2х(0,5 + 0,5x²)
0,001 + x³ = x + x³
x = 0,001;

в) (3z – 2)² = 9(z – 2)(z + 3) – 5
9z² – 12z + 4 = 9z² + 27z – 18z – 54 – 5
–12z – 9z = –5 – 4
–21z = –9

г) (х³ + х² + х + 1)(x – 1) = х⁴ + 10x
x⁴ – x³ + x³ – x² + x² – x + x – 1 = x⁴ + 10x
10x = –1
10x = –1
x = –0,1;
\begin{aligned}
& \text { r) } \frac{2}{3} x-\left(\frac{2}{3} x-3\right)\left(\frac{4}{9} x^2+2 x+9\right)=\frac{4}{9} x\left(6-\frac{2}{3} x^2\right) \\
& \frac{2}{3} x-\frac{8}{27} x^3+27=\frac{8}{3} x-\frac{8}{27} x^3 \\
& \frac{8}{3} x-\frac{2}{3} x=27 \\
& 2 x=27 \\
& x=27: 2 \\
& x=13,5
\end{aligned}

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