If x^2-10 a x-11 b=0 have roots c and d and x^2-10 c x-11 d=0 have roots a and b , then, find a+b+c+d .

Step-by-step solution

Here, a+b=10 c c+d=10 a On subtracting Eq. (ii) from Eq. (i), we get, (a-c)+(b-d)=10(c-a) (b-d)=11(c-a) Since, c is the root of x^2-10 a x+11 b=0 c^2-10 a c-11 b=0 Similarly, a is the root of aligned & x^2-10 c x+11 d=0 & a^2-10 c a-11 d=0 aligned On subtracting Eq. (v) from Eq. (iv), we get aligned & (c^2-a^2 )=11(b-d) & (c+a)(c-a)=11 11(c-a) from (i) & (ii) & c+a=121 . & a+b+c+d=10 c+10 a & =10(c+a)=1210 & aligned