a and b be distinct 3 digits even numbers such that same three digits are used in a and b. If their difference is a two-digit number n, which is a perfect square, find the value of n.
Answers
Given: a and b be distinct 3 digits even numbers such that same three digits are used in a and b.
their difference is a two-digit number n, which is a perfect square,
To find : the value of n.
Solution:
a = xyz
b = xzy
Assuming 1st digit remains same
Difference = 10y + z - 10z - y
= 9 ( y - z)
y and z are even and distinct
Hence possible
9 (2) = 18 , 9(4) = 36 , 9(6) = 54 , 9(8) = 72
only 36 is perfect square
Hence n = 36
Case 2 :
a = xyz
b = yxz
Difference = 100x + 10y - 100y - 10x
= 90(x - y)
x - y = 1 is only possible for 2 digit number but 90 is not perfect square
case 3 :
a = xyz
b = zyx
Difference = 100x + z - 100z - x
= 99 (x - z)
x - z = 1 is only possible for 2 digit number but 99 is not perfect square
so only answer is 36
few possible a and b
126 , 162
148 , 184
104 , 140
204 , 240
248 , 284
and so on
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Answer:
555
Step-by-step explanation:
a and b be distinct 3 digits even numbers such that same three digits are used in a and b. If their difference is a two-digit number n, which is a perfect square, find the value of n.