Question

x= √ 5 +√4 ÷ √5 - √4 , y= √5 - √4 ÷ √ 5+ √4 then x^2+y^2 is​

Answer 1

Answer:

Step-by-step explanation:

x = √5 +√4/√5 - √4

   = [√5 +√4/√5 - √4] * [√5 +√4/√5+√4]

   = (√5 + √4)²/ 5 - 4 = (√5 + √4)² = 9 + 2√20 = 9 + 4√5.

y =   √5 - √4/√5 + √4

    = [√5 - √4/√5 +√4] * [√5 - √4/√5 - √4]

    = (√5 - √4)²/5 - 4 = (√5 - √4)² = 9 - 4√5.

x²+y² = (x + y)² - 2xy

        =  (9 + 4√5 + 9 - 4√5)² - 2(9 + 4√5)(9 - 4√5)

         = (18)² - 2(81-80)

         = 324 - 2

          = 322.