if X = √3-√2/√3+√2 and Y= √3+√2/√3-√2 , find the value of X^2 + Y^2 +XY
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First rationalise X and Y
X = (✓3-✓2)² / 3-2 = (✓3-✓2)² / 1 = (✓3-✓2)²
Y = (✓3+✓2)² / 3-2 = (✓3+✓2)² / 1 = (✓3+✓2)²
X²+Y²+XY = ( (✓3-✓2)²)² + ( (✓3+✓2)²)² + (✓3-✓2)²* (✓3+✓2)²
From here you need to use simple identities and solve it
X = (✓3-✓2)² / 3-2 = (✓3-✓2)² / 1 = (✓3-✓2)²
Y = (✓3+✓2)² / 3-2 = (✓3+✓2)² / 1 = (✓3+✓2)²
X²+Y²+XY = ( (✓3-✓2)²)² + ( (✓3+✓2)²)² + (✓3-✓2)²* (✓3+✓2)²
From here you need to use simple identities and solve it
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