Question

Express the square number 625 as the sum of two triangular numbers

Answer 1

Hey Dear,

◆ 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 .

Thanks dear...

Answer 2

Step-by-step explanation:

Hope it can help you

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