The equation x^2+bx+c=0 has distinct roots.if 2 is subtracted from each root, the results are reciprocals of the original roots. then the value of (b^2+c^2+ bc) ?

let the roots be a and b.

now subtracting 2 from each root ..

a-2 &b-2 r equal to reciprocal of original roots i.e a&b .

so,a-2=1/a &b-2=1/2

solving we get a=& b=1±√2

so we take a=1+√2 & b=1-√2

so

b^2+c^2+bc=(-a-b)² +ab² +(-a-b)*ab=4+1+2=7

hence the answer is 7