Answer:
Hello,
50/4
Step-by-step explanation:
[tex]a^2-b^2=12\ \Longrightarrow\ (a-b)(a+b)=12\\(a-b)^2=9 \ \Longrightarrow\ a-b=3\ or\ a-b=-3\\1) if\ a-b=3:\\\\a+b=\dfrac{12}{3} =4\\\left\{\begin{array}{ccc}a+b&=&4\\a-b&=&3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&\dfrac{7}{2} \\\\b&=&\dfrac{1}{2} \\\end {array} \right.\\\\\\a^2+b^2=(\dfrac{7}{2} )^2+(\dfrac{1}{2} )^2=\dfrac{50}{4}[/tex]
[tex]2) if\ a-b=-3:\\\\a+b=\dfrac{12}{-3} =-4\\\left\{\begin{array}{ccc}a+b&=&-4\\a-b&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&\dfrac{-7}{2} \\\\b&=&\dfrac{-1}{2} \\\end {array} \right.\\\\\\a^2+b^2=(\dfrac{-7}{2} )^2+(\dfrac{-1}{2} )^2=\dfrac{50}{4} \\\\[/tex]
