Question

1) и вычислите 2)решите систему уравнений

Answer 1

1
$3^4*5^4/(3^4*5^2*5^2)=1$
$(5^3*7^7*2^3*3^3*2^6/(2 ^{12} *3^3*7^3*5^2)=5/2^3=5/8$
2
{x²-10x+25-y²+6y-9-x²+y²=0⇒-10x+6y=-16
{5x+3y=15/*2⇒10x+6y=30
прибавим
12y=14
y=7/6
5x+3,5=15
5x=11,5
x=2,3
(2,3;1 1/6)

Answer 2

1)
$\frac{15^4}{3^4*5^2*25}= \frac{3^4*5^4}{3^4*5^2*5^2}=1$

$( \frac{35}{48} )^3*( \frac{6}{7} )^3*(-1 \frac{3}{5} )^2= \\ \\ = \frac{(5*7)^3}{(16*3)^3}* \frac{(2*3)^3}{7^3}*(- \frac{8}{5} )^2= \\ \\ = \frac{5^3*7^3}{(2^4)^3*3^3}* \frac{2^3*3^3}{7^3}* \frac{(2^3)^2}{5^2}= \\ \\ = \frac{5^3*7^3*2^3*2^6*3^3}{5^2*7^3*2^{12}*3^3}= \frac{5}{2^3}= \frac{5}{8}$

2)
(x-5)²-(y-3)²=x²-y²
x²-10x+25-(y²-6y+9)=x²-y²
x²-x²-y²+y²-10x+6y=-16
-10x+6y=-16
-2(5x-3y)= -16
5x-3y=8
5x=8+3y

8+3y+3y=15
6y=15-8
6y=7
y=7/6
y=1 ¹/₆

5x+3* ⁷/₆=15
5x + ⁷/₂ =15
5x=15-3.5
5x=11.5
x=2.3

ответ: (2,3;  1 ¹/₆)