Question

ab= 5, a-b=4, . find (A3+b3)​

Answer 1

Given: ab=5

a-b=4....(A)

Solution: We have a-b=4

Squaring, we get

a²+b²-2ab=16

a²+b²-10=16 (since ab=5)

a²+b²=26...(1)

But we know that

(a+b)²=a²+b²+2ab

OR

a²+b²= (a+b)²-2ab

Using this, we can modify (1) as

(a+b)²-2ab=26

(a+b)²-10=26

(a+b)²=36

a+b = ±6...(B)

Solving (A) and (B), we get

a=5, b=1

OR

a= -1, b= -5

Hence a³+b³=126. OR. a³+b³= -126

Hope it helps