Question

a^3-b^3 = 513 and ab = 54 then find a , b equal to

Answer 1

Answer:

a³ - b³ = 513 and ab = 54

Step-by-step explanation:

Now,

a³-b³ = 513

or, a³-(54/a)³ = 513

or, (a⁶-157464)/a³ = 513

or a⁶- 157464 = 513a³

or, a⁶ - 513a³ - 157464 = 0

or, (a³)² - 729a³ + 216a³ - 157464 = 0

or, a³ (a³- 729) + 216 (a³- 729) = 0

or, (a³ - 729) (a³ + 216) = 0

It becomes, a³ - 729=0 or, a³ = 729 or, a³ = 93 or, a=9

or, a³+216=0 or, a³ = -216 or, a³ = -63 or, a = -6

Now,

a=9 then, b=54/9= 6

Now,

then, b=54/(-6)= -9

Now,

if, (a,b)=(9,6) then, a-b= 9-6= 3

if, (a,b)=(-6,-9) then, a-b= -6-(-9)= -6+9= 3