Find the four digit number or number(s) satisfying this criteria
- The number is a perfect square - WXYZ
- If the Square root of the number is AB, then (A*A) + B = WX and (B*B) = YZ
Please note that there could be more than one correct answer for the above condition
i guess 45 wont come in the solution set.
ReplyDeletefro the eqs
A*A+B=WX--->1
B*B=YZ --->2
OPERATION:100(EQ1)+EQ2
100A*A+100B+B*B=100(WX)+YZ= WXYZ(THE ORIGINAL NUM)=(10A+B)*(10A+B)=100A*A+20AB+B*B
=>A=5
FYI:This is actually a short cut for finding suares of num starting with 5
51^2=5^2+1, 1^2=2601
52^2=5^2+2, 2^2=2704
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59^2=5^2+9, 9^2=3481
similar short cut for sq starting with 4
(1,9)(2,8)(3,7)(4,6)(5,5)
are square pairs
41^2=(4^2-1)+1, 9^2= 1681
42^2=(4^2-1)+2, 8^2=1764
43^2=(4^2-1)+3, 7^2=1849
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49^2=(4^2-1)+9, 1^2= 2401