Question

if y^2+1/y^2=11 find y

Answer 1

Answer:

y = $\frac{3+\sqrt{13} }{2}$

Step-by-step explanation:

given, y²+(1/y²)=11 --------- (1)

(1) => (y - (1/y) )² + 2y(1/y) = 11

=>  (y - (1/y) )² + 2 = 11

=>  (y - (1/y) )²  = 11 - 2

=>  (y - (1/y) )²  = 9 = 3²

=> y - (1/y) = 3 ------------- (2)

(1) => (y + (1/y) )² - 2y(1/y) = 11

=>  (y + (1/y) )² - 2 = 11

=>  (y + (1/y) )²  = 11 + 2

=>  (y + (1/y) )²  = 13

=> y+ (1/y) = √13      ------------ (3)

(2) + (3) = >  

[y - (1/y)] + [y+ (1/y)] = 3+√13

y + y = 3+√13

2y = 3+√13

y = $\frac{3+\sqrt{13} }{2}$