Question

(a-b)=5 and ab=3 then a³‐b³=‐‐----‐‐

15


72


80


18​

Answer 1

✑ ɢɪᴠᴇɴ :-

A + B = 5

AB = 3

✑ ᴛᴏ ғɪɴᴅ :-

A³ + B³ = ?

✑ sᴏʟᴜᴛɪᴏɴ :-

We know that,

➢ (A + B) ³ = A³ + B³ + 3AB(A + B)

So,

Put the above given values in it, we get

→ (5)³ = A³ + B³ + 3×3(5)

→ 125 = A³ + B³ + 45

→ A³ + B³ = 125 - 45 = 80

Hence,

➥ A³ + B³ = 80

➲ More Identities :-

• ( a + b) ² = a² + b² + 2ab

• ( a - b) ² = a² + b² - 2ab

• (a + b) (a - b) = a² - b²

• ( a + b) ³ = a³ + b³ + 3ab ( a + b)

• ( a - b) ³ = a³ - b³ - 3ab (a - b)

Answer 2

Answer:

Step-by-step explanation:

The question asks us to find a^3-b^3, given that

a - b = 5                      ...(i)

ab = 3                         ... (ii)

now, in equation (i), cube both sides

(a-b)^3 = 5^3

a^3 - b^3  - 3ab(a - b) = 125

subtitute values for a-b and ab

a^3 - b^3 -3(3)(5) = 125

a^3 - b^3 - 45 = 125

a^3 - b^3 = 170

(options are given for [a^3 + b^3

which is

a^3 + b^3 + 3ab(a+b) = 125

a^3 + b^3 + 3(3)(5) = 125

a^3 + b^3 = 125 - 45

a^3 + b^3 = 80

hope this helps