Question

ПОМОГИТЕ РЕШИТЬ СИСТЕМУ!
1). 3^1+log3 (x^2-y^2)=15
2). log2 (x^2-y^2)-log2 (x+y)=0

Answer 1

1) 3^1  * 3^log3_(x^2 - y^2)  = 15;
3 *(x^2 - y^2) = 15;
x^2 - y^2 = 5.

2) log2_ (x^2- y^2) / (x + y) = 0;
log 2_(x+y)(x-y) / (x+y) = 0;
log2_(x-y) = 0;
log2_(x-y) = log2_1;
x - y = 1;
 x^2 - y^2 = 5;
(x-y)(x+y) = 5;
1 * ( x + y) = 5;
x + y = 5.
 {x- y = 1;       
   x + y = 5;      2x = 6;
                          x = 3.         y = 5 - x = 5 - 3 = 2.
Ответ х = 3; у = 2