Question

If a + b = 5then find the value of a^3 + b^3 + 15ab.​

Answer 1

Answer:

$\huge\underline{\rm\red{Reticent_Bliss}}$

Step-by-step explanation:

$\huge\underline\green{Given}$ ,

• a + b = 5

$\huge\underline\green{Find}$ ,

• a³ + b³ + 15a

$\huge\underline\pink{We~know~that}$ ,

• (a + b) ³ = a³ + b³ + 3ab ( ab)

$\huge\underline\green{Apply~above~formula}$

• (a + b)³ = a³ + b³ + 3ab ( ab)
• (5)³ = a³ + b³ + 3ab ( 5 )
• 125 = a³ + b³ + 15ab

:. The value of a³ + b³ + 15ab = 125

$\huge\underline\pink{Proof}$ :-

RHS :- a³ + b³ + 15ab

a³ + b³ + 15ab = (a + b) (a² - ab + b²) + 15ab

Put a + b = 5 in above RHS formula,

• 5 (a² - ab + b²) + 15ab
• 5a² - 5ab + 5b² + 15ab
• 5a² + 10ab + 5b²
• 5 ( a² + 2ab + b² ) → equation 1

$\rm\underline\green{From~formula}$ :-

(a + b)² = a² + 2ab + b²

• 5 ( a + b )²
• 5 ( 5 )²
• 5 × 25
• 125

$\huge\green{Hence~U~got}$ ......... ✔

$\huge\underline{\rm\red{Reticent_Bliss}}$

Answer 2

Step-by-step explanation:

Given,

• a + b = 5

We know,

• (a + b) ³ = a³ + b³ + 3ab ( ab)

Applying above formula qq

• (a + b)³ = a³ + b³ + 3ab ( ab)
• (5)³ = a³ + b³ + 3ab ( 5 )
• 125 = a³ + b³ + 15ab

:. The value of a³ + b³ + 15ab = 125