Question

If x=(2-√5)\(2+√5) and y=(2+√5)\(2-√5) then find x² +y²​

Answer 1

Answer:

2

Step-by-step explanation:

x=(2-$\sqrt{5}$)(2+$\sqrt{5\\}$)=2^2-$\sqrt{5\\}$^2=4-5=-1

y=(2+$\sqrt{5}$)(2-$\sqrt{5\\}$)=2^2-$\sqrt{5\\}$^2=4-5=-1

therefore,x^2=y^2=(-1)^2+(-1)^2=1+1=2

Answer 2

Answer:

x² +y²​ = 2

Step-by-step explanation:

x=(2-√5)\(2+√5)

x =(2)^2 - (√5)^2 = 4 -5 = -1            (a^2 - b^2 = (a-b)(a+b))

y =(2+√5)\(2-√5)

y = (2)^2 - (√5)^2 = 4 - 5 = -1

therefore,

x^2 + y^2 =(-1)^2 +(-1)^2 = 1 + 1 = 2