Question

if a^2 + b^2 + 1/a^2 + 1/b^2 = 4 then the value of whole root a^2 + b^2 is

Answer 1

(a^2+b^2+a^-2+b^-2)=4

or. (a^2+b^2+1/a^2+1/b^2)=4

or. a^2+1/a^2-2 +b^2+1/b^2-2=4–2–2

or. (a-1/a)^2+(b-1/b)^2=0……………………..(1)

Comparing the eqn.(1) both side

(a-1/a)^2=0. or. a-1/a=0. or. a=1/a. or. a^2 = 1………………(2)

(b-1/b)^2=0. or. b-1/b=0. or. b=1/b. or. b^2 = 1………………(3)

On subtracting eqn.(3). from. eqn. (2)

(a^2-b^2)=0.

Answer 2

Step-by-step explanation:

(a^2+b^2+a^-2+b^-2)=4

or. (a^2+b^2+1/a^2+1/b^2)=4

or. a^2+1/a^2-2 +b^2+1/b^2-2=4–2–2

or. (a-1/a)^2+(b-1/b)^2=0……………………..(1)

Comparing the eqn.(1) both side

(a-1/a)^2=0. or. a-1/a=0. or. a=1/a. or. a^2 = 1………………(2)

(b-1/b)^2=0. or. b-1/b=0. or. b=1/b. or. b^2 = 1………………(3)

On subtracting eqn.(3). from. eqn. (2)

(a^2-b^2)=0. Answer.

Hope this helps .....