Question

The sum of two number is 25 and their difference is 13. Find their product.

Answer 1

let the numbers be x and y

ATQ
x+y=25—(1)
x-y=13—(2)

adding (1) and (2)
2x=38
x=19

in equation (1)
x+y=25
19+y=25
y=25-19=6

so,
product=xy=19×6=114

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Answer 2

the formula :-

(x+y)² = (x-y)² + 4xy

⇔ (25)² = (13)² + 4xy

⇒ 625 = 169 + 4xy

⇒ 4xy = 625 - 169

⇒ xy = 456/4 

∴ xy = 114


The product of the two numbers is 114