Factorise x ^ 4 + 1/x ^ 4 - 3

Dplusm asked Mar 19, 2022

3,594 views

18 votes

Dplusm asked Mar 19, 2022

2.8k points

Your comment on this question:

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Email me at this address if my answer is selected or commented on:Email me if my answer is selected or commented on

Privacy: Your email address will only be used for sending these notifications.

16 votes

Answer:

Explanation:

Add 1 and subtract 1, so that the expression won't change.

$x^(4)+(1)/(x^(4))-3=x^(4)+(1)/(x^(4))-3 +1 - 1\\\\=x^(4)+(1)/(x^(4)) - 2 + 1\\\\= (x^(2))^(2) + ((1)/(x^(2)))^(2)- 2 *x^(2)*(1)/(x^(2)) - 1\\\\$

$= (x^(2) -(1)/(x^(2)))^(2) - 1\\\\=(x^(2)-(1)/(x^(2)))^(2)- 1^(2)$

(a² - b²) = (a+b)(a - b)

Here a = x² - (1/x²) and b = 1

= [ (x^(2)-(1)/(x^(2)))+ 1 ] [ (x^(2) -(1)/(x^(2)) - 1 ]

Prasanjit Dey answered Mar 24, 2022

2.8k points

Email me at this address if a comment is added after mine:Email me if a comment is added after mine

Privacy: Your email address will only be used for sending these notifications.

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

1.6m questions

2.0m answers