Question

Si: a + b = 5
ab = 2
Hallar: a⁴+b⁴​

Answer 1

Respuesta:

433

Explicación paso a paso:

Aplicas productos notables:

(a+b)² = a² + 2ab + b² = a² + b² + 4

a² + b² = (a+b)² - 4 = 21

(a² + b²)² = a⁴ + 2a²b² + b⁴ = a⁴ + b⁴ + 2(ab)²

(a² + b²)² = a⁴ + b⁴ + 2(2)²

a⁴ + b⁴ = (a² + b²)² - 8

a⁴ + b⁴ = (21)² - 8

a⁴ + b⁴ = 433