Question

If 2y+1/2y=5, then find the value of (a) 4y^2+1/(4y^2 ) (b) 16y^4+1/(16y^4 )

Answer 1

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

2y+1/2y=5 squared both side

$4 {y}^{2} + \frac{1}{4 {y}^{2} } + 2 = 25 \\ 4 {y}^{2} + \frac{1}{4 {y}^{2} } = 23$

(b) 16y^4+1/(16y^4 )

4y^2+1/(4y^2 ) = 23

squared both side

$16 {y}^{2} + \frac{1}{16 {y}^{2} } + 2 = 529 \\16 {y}^{2} + \frac{1}{16 {y}^{2} } = 527$