Question

if 2+ √(5)/2-√(5) =x and 2- √(5)/2+√(5)=y, find the value of x^2-y^2.​

Answer 1

2+ √(5)/2-√(5) =x..................EQ1

2- √(5)/2+√(5)=y....................EQ2

EQ1+EQ2 =>

x+y=2+ √(5)/2-√(5)+2- √(5)/2+√(5) = 4

EQ1-EQ2 =>

x-y=2+ √(5)/2-√(5)-2+√(5)/2-√(5)=√(5)-2√(5)=-√(5)

so ,(x^2-y^2) =(x+y)(x-y)= 4*(-√(5))=-4√(5)

Answer 2

Answer:

Step-by-step explanation:

x=2+√5/2-√5 and y=2-√5/2+√5

rationalising x ,then y

x=2+√5/2-√5×2-√5/2-√5

x=[2]^2-[√5]^2/[2-√5]^2        [using identity a+b×a-b= a^2+b^2, a-b×a-b=[a-b]^2]

  = [2]^2-[√5]^2/[2-√5]^2

  =4-5/4+5-4√5

  =-1/4√5

y=2-√5/2+√5 ×2-√5/2-√5