Question

Find the value using algebraic formula.

`(99813 xx 99815 + 1)/(99814)^2`

Answer 1

Given: `(99813 xx 99815 + 1)/(99814)^2`

Let 99814 = x then 99813 = (x – 1) and 99815 = (x + 1)

∴ `(99813 xx 99815 + 1)/(99814)^2 = ((x - 1) (x + 1) + 1)/x`

We know that,

(a + b) (a – b) = a² – b²

Hence,

⇒ `(x^2 - 1 + 1)/x^2`

⇒ `x^2/x^2`

⇒ 1