Question

If a^1/3-b^1/3=2 and ab=1, then write the value of a^3-b^3

Answer 1

Solution

Given That :-

• a ^(1/3) - b^(1/3) = 2 ------(1)
• ab = 1 -----------------------(2)

Find :-

• Value of a³ - b³

Explanation

First take Cube of equ(1)

➥ a ^(3 × 1/3) - b^(3× 1/3) = 2³

➥ a - b = 8 ---------(3)

Again, take square of equ(3)

➥ (a - b)² = 8²

➥ (a² + b² - 2ab) = 64

➥ a² + b² = 64 + 2ab

keep Value by equ(2)

➥ a² + b² = 64 - 2 × 1

➥ a² + b² = 64 - 2

➥ a² + b² = 62 --------------(4)

Now, Using

★ ( a³ - b³ ) = (a-b)(a²+b²+ab)

keep All above values by equ(2) , (3) & (4)

➥ (a³ - b³ ) = (8)(62+1)

➥ (a³ - b³ ) = 8 × 63

➥ (a³ - b³ ) = 504

Hence

• Value of (a³ - b³ ) be 504

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Answer 2

Answer:

504 is answer of question