Question

Помогите пожалуйста очень срочно надо, умоляю! ​

Answer 1

#1.

$7x^{20}- 567 = 7(x^{20} - 81) = 7(x^{10} - 9)(x^{10} + 9) = 7(x^{5} - 3)(x^5 +3)(x^{10} + 9)$

#2.

a) $S = 6a^2;\\S = 6 * (5a-3)^2 = 6 *(25a^2 - 30a + 9) = 150a^2 - 180a + 54$

б) $V = a^3; V = (5a-3)^3 = (5a-3)(25a^2 - 15a + 9) = 125a^3 - 150a^2 + 90a - 27$

#3.

a) $125^2 - 125 * 50 + 25^2 = (125 - 25)^2 = 100^2 = 10000$

б) $\frac{2500 - 35^2}{65^2 - 20^2} = \frac{50^2 - 35^2}{(65 - 20)(65+20)} = \frac{(50-35)(50+35)}{45 * 85} = \frac{15 * 85}{45 * 85} = \frac{15}{45} = \frac{1}{3}$

#4.

$(x-y) = 45;\\ x^2 - y^2 = 585; (x-y)(x+y) = 585; 45*(x+y) = 585; x + y = 13$

$x - y = 45\\x + y = 13$

$y = x - 45;\\x + x - 45 = 13; 2x = 58; x = 29$

$y = 29 - 45 = -16$

Ответ: x = 29; y = -16.