Question

Answer 1

\(12,\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)=6x\\ x^3-27+5x-x^3-6x=0\\ -x-27=0\\ x=-27\)

\(13,\left(5x-1\right)\left(5x+1\right)=25x^2-7x+15\\ 25x^2-1=25x^2-7x+15\\ x=\dfrac{16}{7}\)

\(14,8x\left(x-3\right)-8\left(x-1\right)\left(x+1\right)=20\\ 8x^2-24x-8x^2+8-20=0\\ x=\dfrac{1}{2}\)

\(15.-4x^2\left(x-7\right)+4x\left(x^2-5\right)=28x^2-13\\ -4x^3+28x^2+4x^3-20x-28x^2=-13\\ x=\dfrac{13}{20}\)

\(16,\left(4x-5\right)\left(x+1\right)-\left(3x-1\right)\left(x+1\right)=x-4\\ \left(x+1\right)\left(4x-5-3x+1\right)=x-4\\ \left(x+1\right)\left(x-4\right)=x-4\\ x^2-3x-4=x-4\\ x\left(x-4\right)=0\\ \left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)

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Answer 2

12. (x - 3)(x² + 3x + 9) + x(5 - x²) = 6x

<=> x³ - 27 + 5x - x³ = 6x

<=> x³ - x³ + 5x - 6x = 27

<=> -x = 27

<=> x = -27

13. (5x - 1)(5x + 1) = 25x² - 7x + 15

<=> 25x² - 1 = 25x² - 7x + 15

<=> 25x² - 25x² + 7x = 15 + 1

<=> 7x = 16

<=> \(x=\dfrac{16}{7}\)

14. 8x(x - 3) - 8(x - 1)(x + 1) = 20

<=> 8x(x - 3) - 8(x² - 1) = 20

<=> 8x² - 24x - 8x² + 8 = 20

<=> 8x² - 8x² - 24x = 20 - 8

<=> -24x = 12

<=> x = \(\dfrac{-1}{2}\)

15. -4x²(x - 7) + 4x(x² - 5) = 28x² - 13

<=> -4x³ + 28x² + 4x³ - 20x = 28x² - 13

<=> -4x³ + 4x³ + 28x² - 28x² - 20x = -13

<=> -20x = -13

<=> \(x=\dfrac{13}{20}\)

16. (4x - 5)(x + 1) - 4(x - 1)(x + 1) = 7

<=> 4x² + 4x - 5x - 5 - 4(x² - 1) = 7

<=> 4x² - x - 5 - 4x² + 4 = 7

<=> 4x² - 4x² - x = 7 + 5 - 4

<=> -x = 8

<=> x = -8