Question

Find the values of a2+ b2 and a4+b4 when a + b = 5 and
ab = 4
​

Answer 1

Answer:

a² + b² = 17

a⁴ + b⁴ = 257

Step-by-step explanation:

We know that,

a + b = 5 and ab = 4

(a + b)² = 5²

a² + 2ab + b² = 25

a² + b² = 25 - 2(ab)

Thus,

a² + b² = 25 - 2(4)

a² + b² = 25 - 8

∴ a² + b² = 17

Now, we have a² + b² = 17

then

(a² + b²)² = 17²

(a²)² + (2 × a² × b²) + (b²)² = 289

We know that, (a^m)^n = a^(m×n) = a^mn

so, we get

a⁴ + 2a²b² + b⁴ = 289

also, we know that (a^m) × (b^m) = (a × b)^m

a⁴ + 2(ab)² + b⁴ = 289

a⁴ + 2(4)² + b⁴ = 289

a⁴ + b⁴ + 32 = 289

a⁴ + b⁴ = 289 - 32

∴ a⁴ + b⁴ = 257

Hope it helped and you understood it........All the best