Question

If a-b=7 and a 2 +b 2 =85 then find the value of a 3 -b 3

Answer 1

Known :
a-b=7 ⇒a=7+b .....(i)
a²+b²=85  ....(ii)

Substitution of equation 1 to equation 2.
(7+b)²+b² =85 
49+14b +b²+b² =85
2b²+14b-36 =0
  b² +7b -18 =0
 (b+9)(b-2) =0
b=-9 v b=2

Find value of a
a-b=7
⇒if b=-9
a-(-9)=7
a =7-9
   =-2
⇒if b=2
a-2=7
a = 7+2
   =9

So value of a³ - b³ there are 2 options
⇒if (a,b) = (-2,-9)
a³-b³ = -2³ - (-9)³
         = -8 +729
         = 721

⇒if (a,b) = (2,9)
a³-b³ = 2³ - 9³  
         = 8-729
         = -721



O_O