Question

if a-b=7 and a^2+b^2=85 then find the value of a^3-b^3​

Answer 1

Answer:

Step-by-step explanation:

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

Answer 2

hope it will help u..............