factorise a²+1-(6/a²)please give me the correct answer with steps please dont just answer for points About the author Jasmine
[tex]\huge \boxed{ \fcolorbox{cyan}{black}{ \: \: \: \: \: ❥anՏwer༻ \: \: \: \: \: }}[/tex] Given: [tex]a^2 + 1 – \frac{6}{a^2} = 0a2+1−a26=0[/tex] To Find: Factories the given equation. Solution: [tex]⇒ a^2 + 1 – \frac{6}{a^2} = 0a2+1−a26=0[/tex] [tex]⇒ \frac{a^4 + a^2 – 6 }{a^2} = 0a2a4+a2−6=0[/tex] [tex] ⇒ a^4 + a^2 – 6 = 0a4+a2−6=0[/tex] Rewriting the equation splitting the middle term using the two factors , -2 and 3 ⇒ a^4 – 2a^2 + 3a^2 – 6 = 0a4−2a2+3a2−6=0 ⇒ a^2 (a^2-2) + 3 (a^2 – 2) = 0a2(a2−2)+3(a2−2)=0 ⇒ (a^2-2) (a^2 + 3) = 0(a2−2)(a2+3)=0 This is the desired factorization. Reply
[tex]\huge \boxed{ \fcolorbox{cyan}{black}{ \: \: \: \: \: ❥anՏwer༻ \: \: \: \: \: }}[/tex]
Given:
[tex]a^2 + 1 – \frac{6}{a^2} = 0a2+1−a26=0[/tex]
To Find:
Solution:
[tex]⇒ a^2 + 1 – \frac{6}{a^2} = 0a2+1−a26=0[/tex]
[tex]⇒ \frac{a^4 + a^2 – 6 }{a^2} = 0a2a4+a2−6=0[/tex]
[tex] ⇒ a^4 + a^2 – 6 = 0a4+a2−6=0[/tex]
Rewriting the equation splitting the middle term using the two factors , -2 and 3
⇒ a^4 – 2a^2 + 3a^2 – 6 = 0a4−2a2+3a2−6=0
⇒ a^2 (a^2-2) + 3 (a^2 – 2) = 0a2(a2−2)+3(a2−2)=0
⇒ (a^2-2) (a^2 + 3) = 0(a2−2)(a2+3)=0