Question

If x- 1 /x =5 then, find the value of x^3-1/x^3.

Answer 1

Gɪᴠᴇɴ

x - 1/x = 5

Tᴏ ꜰɪɴᴅ

Value of x³ - 1/x³

Sᴏʟᴜᴛɪᴏɴ

We know identity :

⟼ a³ - b³ = (a - b)³ + 3ab(a - b)

Pᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇꜱ ᴡᴇ ɢᴇᴛ :

⟼ x³ - 1/x³

⟼ (x - 1/x)³ + 3 * x * 1/x(x - 1/x)

⟼ (5)³ + 3 × 5

⟼ 125 + 15

⟼ 140

ᴛʜᴇʀᴇꜰᴏʀᴇ,

Required value = 140 .

Sᴏᴍᴇ ᴍᴏʀᴇ ꜰᴏʀᴍᴜʟᴀꜱ :

➪ a³ + b³ = (a + b)³ - 3ab(a + b)

➪ (a + b)³ = a³ + b³ + 3ab(a + b)

➪ (a - b)³ = a³ - b³ - 3ab(a - b)

➪ (a + b)² = a² + b² + 2ab

➪ (a - b)² = a² + b² - 2ab

Answer 2

Given:

x - 1/x = 5

Find out:

Value of x³ - 1/x³

Putting the value;

x³ - 1/x³

(x - 1/x)³ + 3 × x × 1/x(x - 1/x)

(5)3 + 3 × 5

125 + 15

140

Thus,

Required value = 140.

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