If x = √a + 1 , y = √a − 1 (a

Home » Aptitude » Algebra » Question

If x = √a + 1 , y = √a − 1 (a > 0), then the value of (x⁴ + y⁴ – 2x²y²) is
√a √a

x = √a +	1	, y = √a −	1
	√a		√a

∴ x + y = √a +	1	+ √a −	1
	√a		√a

= 2√a

∴ x − y = √a +	1	− √a +	1
	√a		√a

=	2
	√a

Now,
x⁴ + y⁴ – 2x²y²
= (x² – y²)²
= {(x + y) (x – y)}²

	2√a ×	1		²	= 4² = 16
		√a

If x = √a +	1	, y = √a −	1	(a > 0), then the value of (x⁴ + y⁴ – 2x²y²) is
	√a		√a