Question

If an = n² - 1 and an = 99 then the value of n is _____

Answer 1

Hey dear friend

Given-:
An=n²-1
An=99

To Find-:
Value of n =?

Solution-:

=>99=n²-1
=>99+1=n²
=>100=n²
=>n=10


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Answer 2

Answer:

Required value of n is ±10.

Step-by-step explanation:

Given,$a_n = n² - 1$and $a_n = 99$

So according to question,

${n}^{2} - 1 = 99$

We are separating variable and constant part,

${n}^{2} = 99 + 1$

We are adding 99 and 1,

${n}^{2} = 100$

$n = \sqrt{100}$

So,$n=±10$

This is a problem of Algebra.

Some important formulas of Algebra are

${(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2}$

${(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2}$

${x}^{2} - {y}^{2} = (x + y)(x - y)$

${x}^{2} + {y}^{2} = {(x + y)}^{2} - 2xy$

e.t.c