Question

x/y = y/x +3/2 then x²/y²+y²/x² =?​

Answer 1

Step-by-step explanation:

Given :-

x/y = y/x +3/2

To find :-

Find the value of x²/y²+y²/x² ?

Solution :-

Given that

x/y = y/x +3/2

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

=> [(x×x)-(y×y)]/(xy) = 3/2

=> (x²-y²)/(xy) = 3/2

=> (x+y)(x-y)/(xy) = 3/2

On taking as x = 2 and y = 1 then

=> (2+1)(2-1)/(2×1) = 3/2

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

=> 3/2 = 3/2

The above equation is true for x = 2 and y = 1

Now,

The value of x²/y²+y²/x²

=> (2²/1²)+(1²/2²)

=> (4/1)+(1/4)

=> 4+(1/4)

=> (4×4+1)/4

=> (16+1)/4

=> 17/4

Answer:-

The value of x²/y²+y²/x² is 17/4

Used formulae:-

→ Trail and Error Method.