Question 924875
{{{(a+b)^2=9}}} and {{{(a-b)^2=49}}}: find {{{a}}} and {{{b}}}

{{{(a+b)^2=9}}} ...sqrt of both sides

{{{sqrt((a+b)^2)=sqrt(9)}}}

{{{a+b=3}}} ...solve for {{{a}}}

{{{a=3-b}}} ....eq.1

{{{(a-b)^2=49}}}

{{{sqrt((a-b)^2)=sqrt(49)}}}

{{{a-b=7}}} ...solve for {{{a}}}

{{{a=7+b}}} ...eq.2

from eq.1 and eq.2 => {{{3-b=7+b}}}...solve for {{{b}}}

{{{3-7=b+b}}}
{{{-4=2b}}}
{{{-4/2=b}}}

{{{highlight(b=-2)}}}

now find {{{a}}}

{{{a=7+b}}} ...eq.2

{{{a=7+(-2)}}}

{{{a=7-2}}}

{{{highlight(a=5)}}}
 
the value of {{{a^2+b^2=5^2+(-2)^2=25+4=29}}}