1.

If p+q=5 prove p^3 +q^3 +15pq=125​

Answer»

Given:

↬ p+Q= 5

To Prove:

✏ p³+q³+15pq= 125

Solution:

We know that,

⟼ (a+b)³ =a³ +b³ +3AB(a+b)

⟼  5³ = 125

It is given that

➺ p+q= 5

On cubing both the sides, we get

➺ (p+q)³= 5³

➺ p³+q³+3(p)(q)(p+q)= 125

➺ p³+q³+3pq(p+q)= 125

On putting the value of p+q, we get

➺ p³+q³+3pq(5)= 125

➺ p³+q³+15pq= 125

Hence proved


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