If p and q are prime numbers such that 4p + 5q = a and 5p + 6q = a + 13, where a is a positive integer, then a can be
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is it right??Tell me
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ankitkumar2450pai6dt:
mujhe pata Hota Toh Tere se main puchta
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as far as i know its right
no it is not right correct answer is 63
4p + 5q = a ....(i)
5p + 6q = a + 13 ....(ii)
From (i) and (ii)
q + 52 = a and p = 5a + 11
∴ a = 63
5p + 6q = a + 13 ....(ii)
From (i) and (ii)
q + 52 = a and p = 5a + 11
∴ a = 63
Can you explain further
Answered by
3
Answer:
a = 54 or 63
Step-by-step explanation:
Let, 4p + 5q = a ................ (1)
and 5p + 6q =a + 13 .............. (2)
Multiplying equation (1) by 5 and equation (2) by 4 and then subtracting equation (2) from equation (1) we get :
q = a - 52
By using hit and trial method :
Case 1 : q = 2, then a = 54
Case 2 : q = 3, then a = 55 and so on.
Let us substitute the values of case 1 in equation (1)
We get 4p + 10 = 54
p = 11
Therefore if p,q = 11,2 which are prime numbers then a = 54
Now, interchanging values of p and q such that p = 2 and q = 11.
We get, a = 63.
Therefore the value of a can be 54 or 63.
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