Answered

Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Get quick and reliable solutions to your questions from a community of seasoned experts on our user-friendly platform. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

Find the real or imaginary solutions of the equations by factoring. x^4-26x^2=-25

Find The Real Or Imaginary Solutions Of The Equations By Factoring X426x225 class=

Sagot :

Answer:

x=1, -1, 5, and -5.

Explanation:

Given the equation:

[tex]x^4-26x^2=-25[/tex]

First, bring the constant term to the left-hand side of the equation:

[tex]x^4-26x^2+25=0[/tex]

Next, rewrite the middle term using factors of 25x⁴.

[tex]x^4-25x^2-x^2+25=0[/tex]

Factor the first two and last two terms:

[tex]\begin{gathered} x^2(x^2-25)-1(x^2-25)=0 \\ (x^2-1)(x^2-25)=0 \\ (x^2-1)(x^2-5^2)=0 \end{gathered}[/tex]

Using the principle of difference of two squares: a²-b²=(a-b)(a+b)

[tex]\begin{gathered} (x-1)(x+1)(x-5)(x+5)=0 \\ \implies x-1=0\text{ or }x+1=0\text{ or }x-5=0\text{ or }x+5=0 \\ \operatorname{\implies}x=1\text{ or }x=-1\text{ or }x=5\text{ or }x=-5 \end{gathered}[/tex]

The solutions are 1, -1, 5, and -5.

We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.