Question

if x= 1+√2+√3 and y=1+√2-√3 then x²+4xy+y²÷x+y

please help ​

Answer 1

Answer:

Hence, (x²+4xy+y²) /(x+y) = (6)/(3) = 12(1+√2) / 2(1+√2) = 6.

Step-by-step explanation:

x=1+√2+√3 …(1) and

y=1+√2–√3 …(2)

Add (1) and (2): (x+y) = 2 +2√2 = 2(1+√2)…(3)

Square of (3) = x^2+2xy+y^2 = 4+8√2+8 = 12+8√2 …(4)

From (1) and (2): xy = {(1+√2)+√3}{(1+√2)-√3}

= [1+2√2+2–3]

= 2√2

and 2xy = 4√2 …(5)

Add (4) and (5): x^2+2xy+y^2+2xy = 12+8√2 + 4√2 = 12+12√2 = 12(1+√2)…(6)

Hence, (x²+4xy+y²) /(x+y) = (6)/(3) = 12(1+√2) / 2(1+√2) = 6.