Question

If x=2-✓5/2+✓5 y=2+✓5/2-✓5 find the value of x²-y ²

Answer 1

Answer:

Step-by-step explanation:

(x+y)²=x²+xy+y²

x²+xy+y²={(√5-√2÷√5+√2)+(√5+√2÷√5-√2)}²

x²+xy+y²={(√5-√2)(√5-√2)+(√5+√2)(√5+√2)÷(√5+√2)(√5-√2)}²

as we know that,

(a+b)²=(a+b)(a+b)

(a-b)²=(a-b)(a-b)

(a+b)(a-b)=a²-b²

so,x²+xy+y²={(√5-√2)²+(√5+√2)²÷(√5)²-(√2)²}²

x²+xy+y²=[{(√5)²-(√2)²}²÷5-3]²

x²+xy+y²={(5-2)²÷3}²

x²+xy+y²={(3)²÷3}²

x²+xy+y²={9÷3}²

x²+xy+y²=(3)²

x²+xy+y²=9

Answer 2

Step-by-step explanation:

4root 5

I hope this answer is right