Question

if (a+1/a+2)^2 = 4. then find a^2+(1/a)^2, given that (a^2 + (1/a)^2) cannot be negative

Answer 1

(a+1/a+2)²= 4

a²+ 1 + 2a/a²+ 4 + 4a. =. 4


a²+ 1 + 2a. =. 4(a² + 4. +4a )

a² + 1 + 2à. =. 4a². + 16. + 16a


0. =. 4a² - a². + 16 - 1. + 16a - 2a

0= 3a². + 15. + 14a

0 =. 3a² + 14a. + 15

0= 3a² + 9a + 5a + 15

0. =. 3a(a+3) +5(a+3)

0. = (a+3)(3a+5)

a = -3
a= -5/3



then the value of ,


when a=-3

a²+(1/a)² = (-3)² +. (-1/3)²


= 9 + 1/9


= (81+1)/9


=. 82/9



and when a= -5/3,



a²+1/a² =. (-5/3)²+(1/-5/3)²

=. 25/9 + 9/25


=. (625+81)/225

= 706/225






I hope it is helpful for you



please mark it as brainliest answer if you have satisfied

Answer 2

Step-by-step explanation:

answer is 14 I hope it helps you yoyo