Question

if x^2+y^2=13 and xy=6 find x^4+y^4​

Answer 1

x⁴ + y⁴ = 97

Step-by-step explanation:

x² + y² = 13

Squaring both the sides,

(x² + y²)² = (13)²

→ (x²)² + (y²)² + 2x²y² = 169

• x²y² = (xy)²

From Question, xy = 6

Hence, x²y² = (xy)² = (6)²

→ x⁴+ y⁴ + 2(6)² = 169

→ x⁴+ y⁴ + 2(36) = 169

→ x⁴+ y⁴ + 72 = 169

→ x⁴+ y⁴ = 169 - 72

→ x⁴+ y⁴ = 97

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Identity used :

• (a + b)² = a² + b² + 2ab