Question

PLEASE NEED HELP:(
a square - b square=12 (a-b) square = 9 what is a square + b square

Answer 1

Hello,

50/4

Explanation:

`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=(12)/(3) =4\\\left\{\begin{array}{ccc}a+b&=&4\\a-b&=&3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&(7)/(2) \\\\b&=&(1)/(2) \\\end {array} \right.\\\\\\a^2+b^2=((7)/(2) )^2+((1)/(2) )^2=(50)/(4)`

`2) if\ a-b=-3:\\\\a+b=(12)/(-3) =-4\\\left\{\begin{array}{ccc}a+b&=&-4\\a-b&=&-3\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&(-7)/(2) \\\\b&=&(-1)/(2) \\\end {array} \right.\\\\\\a^2+b^2=((-7)/(2) )^2+((-1)/(2) )^2=(50)/(4) \\\\`