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Let a, b, c and d be four roots of the equation x^4-10 x^3+37 x^2-60 x+32=0 . If 1 a^2-5 a+10 + 1 b^2-5 b+10 + 1 c^2-5 c+10 + 1 d^2-5 d+10 = p q , where p and q are co-prime numbers, then find the value of (p+q) .

Correct answer

7

Step-by-step solution

aligned & (x^2-5 x+10 ) (x^2-5 x+2 )+12=0 & (x^2-5 x+10 ) (x^2-5 x+10-8 )+12=0 & (x^2-5 x+10 )^2-8 (x^2-5 x+10 )+12=0 & x^2-5 x+10=2,6 & 1 a^2-5 a+10 = 2 2 + 2 6 = 4 3 = p q & p+q=7 aligned

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