Question

If a+b=(-5) and ab=(-6) then what is the value of a³-b³ where a>b?

Answer 1

please ignore my writing

Answer 2

SOLUTION :-

Given ,

• a + b = - 5 ..eq(1)
• ab = - 6 ..eq(2)

To find ,

• a³ - b³ = ?

✤ Squaring on Both sides for eq(1)

☞ ( a + b )² = ( - 5 )²

☞ a² + b² + 2ab = 25

☞ a² + b² = 25 - 2 ( - 6 )

☞ a² + b² = 25 + 12

☞ a² + b² = 37

♦ ( a - b )² = a² + b² - 2ab = 37 - 12 = 25

♦ ( a - b)² = 25

♦ a - b = √25 = 5

✤ Now , finding a³ - b³

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

➜ a³ - b³ = 5 [ 37 + (-6) ]

➜ a³ - b³ = 5 [ 37 - 6 ]

➜ a³ - b³ = 5 [ 31 ]

➜ a ³ - b³ = 155