Question

if x=√2+1 and y=√2-1 find the value of x²+y²+xy

Answer 1

this is the answer.....

Answer 2

Hi there!

Given :-

♦ x = √2 + 1
♦ y = √2 - 1

ATQ,

→ x² = (√2 + 1)²

= 2 + 1 + 2(√2)

= 3 + 2√2. ----(i)

→ y² = (√2 - 1)²

= 2 + 1 - 2(√2)

= 3 - 2√2. ----(ii)

→ xy = (√2 + 1) × (√2 - 1)

= (√2)² - (1)²

= 2 - 1

= 1. ----(iii)

Adding eqn. (i), (ii) n' (iii) :-

x² + y² + xy = (3 + 2√2) + (3 - 2√2) + 1

= 3 + 2√2 + 3 - 2√2 + 1

= 3 + 3 + 1

= 7

Hence, The required answer is :-
x² + y² + xy = 7

Hope it helps! :)