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

Answer:

(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

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