Answer:50
Explanation:
(\sqrt{x-1} -b-c)/a +(\sqrt{x-1}-c-a)/b+ (\sqrt{x-1}-a-b)/c= 3\\\\
[(\sqrt{x-1} -b-c)*b*c +(\sqrt{x-1}-c-a)*a*c+ (\sqrt{x-1}-a-b)*a*b]/a*b*c= 3\\\
(a*b+b*c+a*c)(\sqrt{x-1)}-b^{2} *c-c^{2}*b-c^{2} *a-a^{2} *c-a^{2}*b-b^{2}*a= 3*a*b*c\\\\
(a*b+b*c+a*c)(\sqrt{x-1)}-b*c(b+c)-c*a(c+a)-a*b(a+b)=3*a*b*c\\
\\
since \\
given that \\
a+b+c=7,\\
a+b =7-c, b+c= 7-a, a+c= 7-b\\
substitute in the given equation\\\\
(a*b+b*c+a*c)(\sqrt{x-1)}-b*c(7-a)-c*a(7-b)-a*b(7-c)=3*a*b*c\\\\
\\(a*b+b*c+a*c)(\sqrt{x-1)}-b*c(7-a)-c*a(7-b)-a*b(7-c)=3*a*b*c\\
(a*b+b*c+a*c)(\sqrt{x-1)}-7(b*c+c*a+a*b)+3*a*b*c=3*a*b*c\\
\\
3*a*b*c \\
cancels\\\\
(a*b+b*c+a*c)((\sqrt{x-1)}-7)=0\\
\\
(\sqrt{x-1)}-7)=0\\
\sqrt{x-1)}=7\\
x-1=49\\
x=50