Question

найдите такие числа а и b,что a+b=ab=a:b​

Answer 1

$\displaystyle\bf\\a+b=ab=a:b\\\\a+b=ab=\frac{a}{b} \\\\\\ab=\frac{a}{b} \ \ \ \Rightarrow \ \ \ ab^{2} =a \ \ \ \Rightarrow \ \ \ ab^{2} -a=0 \ \ \ \Rightarrow \ \ \ a\cdot(b^{2} -1)=0\\\\\\\left[\begin{array}{ccc}a=0\\b^{2} -1=0\end{array}\right \ \ \ \Rightarrow \ \ \ \left[\begin{array}{ccc}a=0\\(b-1)(b+1)=0\end{array}\right \ \ \ \Rightarrow \ \ \ \left[\begin{array}{ccc}a=0\\b_{1} =1\\b_{2} =-1\end{array}\right \\\\\\1) \ \ a=0$

$\displaystyle\bf\\a+b=a\cdot b\\\\0+b=0\cdot b\\\\b=0 \ - \ ne \ podxodit, \ tak \ kak \ b\neq 0\\\\2) \ \ b=1\\\\a+b=a\cdot b\\\\a+1=a\cdot 1\\\\a+1=a\\\\a-a=-1\\\\0\cdot a=-1 \ - \ neverno\\\\3) \ \ b=-1\\\\a+b=a\cdot b\\\\a+(-1)=a\cdot(-1)\\\\a-1=-a\\\\a+a=1\\\\2a=1\\\\a=0,5\\\\\\Otvet \ : \ a=0,5 \ \ ; \ \ b=-1$