Question

Срочно допоможіть будь ласка

Answer 1

Ответ:

1.1) (2a-3b)² = 4a² - 12ab + 9b²

2) (8x³ - 6y)(8x³+6y) = 64$x^{6}$ - 36y²

3) (3$p^{4}$ + 5$k^{6}$)² = 9$p^{8}$ + 30$p^{4}$ $k^{6}$ + 25$k^{12}$

4) ($x^{4}$-x²)² = $x^{8}$ - 2$x^{6}$ + $x^{4}$

5) $(\frac{1}{2}a + b)^{2}$ = $\frac{1}{4}a^{2} + ab + b^{2}$

6) $(x^{9}-y^{5})(y^{5}+ x^{9}) = x^{18} - y^{10}$

2.1) (x - 2)² + (x + 7)² = 2(2 - x)(x + 7)

x² - 4x + 4 + x² + 14x + 49 = 2(2x + 14 - x² - 7x)

2x² + 10x + 53 = 4x + 28 - 2x² - 14x

4x² + 20x + 25 = 0

D = 400 - 4 * 25 * 4 = 400 - 400 = 0

x = -b/2a = -20/8 = $-\frac{5}{2}$

2) (4x-3)² - 25x² = 0

16x² - 24x + 9 - 25x² = 0

-9x² - 24x + 9 = 0

-3x² - 8x + 3 = 0 | :3

D = 64 - 4 * 3 * -3 = 64 + 36 = 100 = 10²

$x_{1} = \frac{8+10}{-6} = \frac{18}{-6} = -3\\x_{2} = \frac{8-10}{-6} = \frac{-2}{-6} = \frac{1}{3}$