Question

If X=/3+1÷/3-1,Xy=1 then find value of x²÷y +y²÷x​

Answer 1

Answer

12

Step by step solution:-

xy=1

Therefore, y=/3-1÷/3+1

x^2=(/3+1)^2÷(/3-1)^

=3+2/3+1÷3-2/3+1

=2+/3÷2-/3

similarly (same as x^2), y^2=2-/3÷2+/3

x+y

=(2+/3÷2-/3)÷(2-/3÷2+/3)

=4

Now,

x²÷y +y²÷x

=x^3+y^3/xy

=(x+y)(x^2-xy+y^2)/xy

(putting the values)

=4[(2+/3÷2-/3)-1+(2-/3÷2+/3)]

=4[(2+/3-4+3+2-/3)÷(4-3)]

=4(3)

=12