Express 64 as the sum of 2 consecutive triangular numbers
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◆ Answer -
625 = 300 + 325
◆ Explanation -
Let x and y be consecutive triangular numbers such that -
x = n(n+1)/2
y = (n+1)(n+2)/2
Here,
x + y = 625
n(n+1)/2 + (n+1)(n+2)/2 = 625
(n+n+2) × (n+1)/2 = 625
(n+1)(n+1) = 25×25
n+1 = 25
n = 24
Now solve for x & y,
x = n(n+1)/2 = 24×25/2 = 300
y = (n+1)(n+2)/2 = 25×26/2 = 325.
Hence, square no 625 can be expressed as sum of two triangular numbers as 625 = 300 + 325 .
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