Math

[Guest]

Find the value of expression
(a+b)²-49s²+2(c+d)(a+b)+(c+d)²
if (a+c+b+d+7s)²+(a+c+b+d-7s)²=0.

[Guest]

[tex](a+c+b+d+7s)^{2 } + (a+c+b+d-7s)^{2 }[/tex]= 0 [tex]\Rightarrow[/tex]

[tex]\begin{array}{|l} a+b+c+d+7s= 0 \\ a+b+c+d-7s = 0 \end{array}[/tex] [we collect and subtract]

[tex]\begin{array}{|l} a+b+c+d=0 \\ s = 0 \end{array}[/tex] [tex]\Rightarrow[/tex]
c+d= -(a+b) (1) , s=0 (2)

[tex](a+b)^{2 }-49 s^{2 } +2(c+d)(a+b)+ (c+d)^{2 }[/tex]=

=[tex](a+b)^{2 }[/tex]-49.0 +2[ -(a+b)](a+b)+ [tex][ - (a+b) ]^{2 }[/tex]=

=[tex](a+b)^{2 } -2 (a+b)^{2 } + (a+b)^{2 }[/tex]=

=[tex]2(a+b)^{2 } - 2(a+b)^{2 }[/tex] = 0