Question

If a b = 3 and a - b =2 then a² - b² =

Answer 1

Hi,

Explanation:

b≠0 because if b=0 then a*b=0 and not 3.

`\left\{\begin{array}{ccc}a*b&=&3\\a-b&=&2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&(3)/(b)\\(3)/(b)-b&=&2\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&(3)/(b)\\3-b^2&=&2b\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}a&=&(3)/(b)\\b^2+2b-3&=&0\\\end {array} \right.\\\\\Delta=4+4*3=16=4^2\\\\b=(-2-4)/(2) =-3 \ or \ b=(-2+4)/(2)=1`

`\\\\\left\{\begin{array}{ccc}b&=&-3\\a&=&-1\\a^2-b^2&=(-1)^2-(-3)^2=1-9=&-8\end {array} \right.\\\\\ or\\\\\left\{\begin{array}{ccc}b&=&1\\a&=&3\\a^2-b^2&=3^2-1^2=9-1=&8\end {array} \right.\\`