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Suppose an integer r , a natural number n and a prime number p satisfy the equation 7 x^2-44 x+12=p^n . Find the largest value of p .

Correct answer

47

Step-by-step solution

array ll 7 x^2-44 x+12=p^n & 7 x^2-42 x-2 x+12=p^n & (7 x-2)(x-6)=p^n & 7 x-2=p^ and x-6=p^ & (7 x-2)-7(x-6)=p^ -7 p^ & 40=p^ -7 p^ & If , N, p is divisors of 40 & p=2 or 5 If p=2,40=2^ -7.2^ & 2^3 .5=2^ -7.2^ =3 and 2^ =40+56 & Z hence not possible If p=5 then 40=5^ -7.5^ & 2^3 .5=5^ -7.5^ =1 and 5^ =40+35 & Z hence not possible so =0 p^ =47 & p=47 and =1 array

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