Question

given( a^2- 7a+ 1)=0 find a^2+1/a^2​

Answer 1

Answer:

a=  -(-7) ±√(-7)²-4(1)(1)/2(1)

a=7±√49-4/2

a=7±√45/2

Now if a=7+3√5/2 then 1/a=2/7+3√5

2(7-3√5)/7²-√45²

14-6√5/49-45

14-6√5/4=7-3√5/2

a^2+1/a^2= (7+3√5/2)² +(7-3√5/2)²=49+45 +42√5 +49+45-42√5/4

188/4=47

Step-by-step explanation:

Answer 2

a^2-7a+1=0

or,a^2+1=7a

now a^2+1/a^2

=(a^4+1)/a^2

=((a^2)^2+(1)^2)/a^2

=((a^2+1)^2-2.a^2.1)/a^2

=((7a)^2-2a^2)/a^2

=(49a^2-2a^2)/a^2

=47a^2/a^2

=47