Question

If x = √2 + 1 / √-1 and y = √ 2 -1 / √ -1 then find the value of x^2 + xy + y^2.

Answer 1

Answer:

=1+3+2root2+3-2root2=3+3+1=7

Step-by-step explanation:

just use a square+ b square +2ab = a+b whole sqaure

Answer 2

Answer:

35

Step-by-step explanation:

Given, x = (√2 + 1)/(√2 - 1)

Now, Multiply by (√2 + 1) in numerator and denominator, we get

x = {(√2 + 1)*(√2 + 1)}/{(√2 - 1)*(√2 + 1)}

=> x = (√2 + 1)² /{(√2)² - 1}

=> x = {(√2)² + 1 + 2√2)}/(2 - 1)

=> x = 2 + 1 + 2√2

=> x = 3 + 2√2

Again given, y = (√2 - 1)/(√2 + 1)

Now, Multiply by (√2 - 1) in numerator and denominator, we get

y = {(√2 - 1)*(√2 - 1)}/{(√2 - 1)*(√2 + 1)}

=> y = (√2 - 1)² /{(√2)² - 1}

=> y = {(√2)² + 1 - 2√2)}/(2 - 1)

=> y = 2 + 1 - 2√2

=> y = 3 - 2√2

Again x*y = (3 + 2√2)*(3 - 2√2)

               = 9 - (2√2)2

               = 9 - 8

               = 1

Now,

x² + y² + x*y

=  (3 + 2√2)² + (3 - 2√2)² + 1

= 9 + 8 + 12√2 + 9 + 8 - 12√2 + 1

= 9 + 8 + 9 + 8 + 1

= 35

So,

x² + y² + x*y = 35

Hope it helps!