Question

if x2 + y2 =29 and xy=2, find the value of x4+y4​

Answer 1

Step-by-step explanation:

( x² + y²)² = (x²)² + (y²)² + 2x²y².

= x⁴ + y⁴ + 2 (xy) (xy).

(29)² = x⁴ + y⁴ + 2 (2) (2).

841. = x⁴ + y⁴ + 8.

so, x⁴ + y⁴ = 841 - 8.

x⁴ + y⁴ = 833.

Answer 2

Step-by-step explanation:

Given :– x²+y² = 29

xy = 2

To Find :– x⁴+y⁴

Solⁿ :–

x²+y² = 29

Squaring both sides

(x²+y²)² = (29)²

⇒(x²)²+(y²)²+2x²y² = 841

⇒x⁴+y⁴+2(xy)² = 841 ------ (i)

Putting xy = 2 in eq(i)

x⁴+y⁴+2×(2)² = 841

⇒x⁴+y⁴+8 = 841

⇒x⁴+y⁴ = 841-8

x⁴+y⁴ = 833