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Answer 1

Answer:

m³ + n³ = 27

Step-by-step explanation:

We have,

m + n = 9

mn = 26

Now,

Let's cube (m + n) as it will only bring us to m³ + n³

So,

m + n = 9

Cubing both sides,

(m + n)³ = 9³

Using the identity,

(a + b)³ = a³ + 3ab(a + b) + b³

Thus,

(m + n)³ = 9³

m³ + 3mn(m + n) + n³ = 729

m³ + 3(mn)(m + n) + n³ = 729

According to what is given,

m³ + 3(26)(9) + n³ = 729

m³ + n³ + 702 = 729

m³ + n³ = 729 - 702

∴ m³ + n³ = 27

Hence,

m³ + n³ = 27

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