Math, asked by Akdasauza1, 1 year ago


x^6 - 1 \div x {2} - 1
solv que.

Answers

Answered by sivaprasath
1
solution:

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Given:

 \frac{x^6 -1}{x^2-1}

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we know that,

a² - b² = (a+b) (a-b)

and 1 power anything is 1,

so,

x^6 - 1 = (x^3 + 1)(x^3 - 1)

x² - 1 = (x+1)(x-1)

By using

a³ + b³ = (a+b) (a² - ab +b²)
a³ - b³ = (a-b) (a² + ab +b²)

(x³+1) =(x+1)(x²- x + 1)

& (x³-1) = (x-1) (x²+x+1)

so,

=>  \frac{x^6-1}{x^2-1} =  \frac{(x^3 +1)(x^3-1)}{(x+1)(x-1)}


=>  \frac{x^6 -1}{x^2-1} = \frac{(x+1)(x^2-x+1)(x-1)(x^2 +x +1)}{(x-1)(x+1)}

=>  \frac{x^6 - 1}{x^2-1} =(x^2 -x+1)(x^2+x+1)

=> \frac{x^6 - 1}{x^2 - 1} =  [(x^2 + 1) -x] [(x^2+1)+x]

=>  \frac{x^6-1}{x^2-1} =  (x^2+1)^2-(x)^2

=>  \frac{x^6 - 1}{x^2-1} = x^4 +2x^2 +1 -x^2

=> \frac{x^6 -1}{x^2 - 1} = x^4 + x^2 + 1

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                                                    Hope it Helps!!
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