Ответ:
1)2x² + 24xy +72y² = 2 ·(х²+12ху+36у²) = 2·(х+6у)² = 2·(х+6у)(х+6у)
2)10ab-5b² -6a+3b=5b(2a-b)-3(2a-b)=(2a-b)(5b-3)
3х^2 - 10х + 3
D=100 - 36 = 8^2
X_1=3
X_2=0.3
3х^2 - 10х + 3=3(х-3)(х-0.3)
1) упростим выражение:
![{x}^{2} ( {x}^{2} - 3x + 1) - 2x( {x}^{3} - 3 {x}^{2} + x) = {x}^{4} - 3 {x}^{3} + {x}^{2} - 2 {x}^{4} + 6 {x}^{3} - 2 {x}^{2} = - {x}^{4} + 3 {x}^{3} - {x}^{2} = - {x}^{2} ( {x}^{2} - 3x + 1)](https://tex.z-dn.net/?f=++%7Bx%7D%5E%7B2%7D+%28+%7Bx%7D%5E%7B2%7D++-+3x+%2B+1%29+-+2x%28+%7Bx%7D%5E%7B3%7D++-+3+%7Bx%7D%5E%7B2%7D++%2B+x%29+%3D++%7Bx%7D%5E%7B4%7D++-+3+%7Bx%7D%5E%7B3%7D++%2B++%7Bx%7D%5E%7B2%7D++-+2+%7Bx%7D%5E%7B4%7D++%2B+6+%7Bx%7D%5E%7B3%7D++-+2+%7Bx%7D%5E%7B2%7D++%3D++-++%7Bx%7D%5E%7B4%7D++%2B+3+%7Bx%7D%5E%7B3%7D++-++%7Bx%7D%5E%7B2%7D++%3D+++-+%7Bx%7D%5E%7B2%7D+%28+%7Bx%7D%5E%7B2%7D++-+3x+%2B+1%29)
2) подставим наше значение х:
![- ({1 \frac{1}{3} )}^{2} \times ( {(1 \frac{1}{3} )}^{2} - 3 \times 1 \frac{1}{3} + 1) = - {( \frac{4}{3} )}^{2} \times ( {( \frac{4}{3} )}^{2} - 3 \times \frac{4}{3} + 1) = - \frac{16}{9} \times ( \frac{16}{9} - 4 + 1) = - \frac{16}{9} \times (1 \frac{7}{9} - 3) = \frac{16}{9} \times ( - 1 \frac{2}{9} ) = - \frac{16 \times 11}{9 \times 9} = - \frac{176}{81} = - 2 \frac{14}{81}](https://tex.z-dn.net/?f=+-+%28%7B1+%5Cfrac%7B1%7D%7B3%7D+%29%7D%5E%7B2%7D++%5Ctimes+%28+%7B%281+%5Cfrac%7B1%7D%7B3%7D+%29%7D%5E%7B2%7D++-+3+%5Ctimes+1+%5Cfrac%7B1%7D%7B3%7D++%2B+1%29+%3D++-++%7B%28+%5Cfrac%7B4%7D%7B3%7D+%29%7D%5E%7B2%7D++%5Ctimes+%28+%7B%28+%5Cfrac%7B4%7D%7B3%7D+%29%7D%5E%7B2%7D++-+3+%5Ctimes++%5Cfrac%7B4%7D%7B3%7D++%2B+1%29+%3D++-++%5Cfrac%7B16%7D%7B9%7D++%5Ctimes+%28+%5Cfrac%7B16%7D%7B9%7D++-+4+%2B+1%29+%3D++-++%5Cfrac%7B16%7D%7B9%7D++%5Ctimes+%281+%5Cfrac%7B7%7D%7B9%7D++-+3%29+%3D++%5Cfrac%7B16%7D%7B9%7D++%5Ctimes+%28+-+1+%5Cfrac%7B2%7D%7B9%7D+%29+%3D++-++%5Cfrac%7B16+%5Ctimes+11%7D%7B9+%5Ctimes+9%7D++%3D++-++%5Cfrac%7B176%7D%7B81%7D++%3D++-+2+%5Cfrac%7B14%7D%7B81%7D+)
Из 1 уравнения выразим у
у= -2/5 + x
подставим у во второе уравнение, получим:
-5x+9(-2/5 + x) = 4
-5x -18/5 + 9x = 4
4x = 38/5
x = 38/20 = 1.9
Теперь, подставим х в у= -2/5 + x
y= -2/5 + 38/20 = (-8+38)/20 = 30/20 = 3/2 = 1.5
И того:
y = 1.5
x = 1.9