Question

If x = √2+1/√2-1 and y= √2-1/√2+1 what is x²+y²

Answer 1

Step-by-step explanation:

x = √2+1/√2-1

y= √2-1/√2+1

1st of all we'll rationalize both x and y

so x= (√2+1)(√2+1)/(√2-1)(√2+1)

=[(√2)²+2(1)(√2)+(1)²]/[(√2)²- (1)²]

=(2+2√2+1)/(2-1)

x=3+2√2

similarly

y = 3-2√2

so

x²+y²= (3+2√2)²+ (3-2√2)²

= (3)²+2(2√2)(3)+(2√2)² + (3)²-2(2√2)(3)+(2√2)²

9+8+4√2-4√2+9+8

=18+16

=34

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Answer 2

Answer:

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