Question

if a + 2 b=3 and ab=-5 then find the value of a^3+8b^3

Answer 1

Hi Friend !!!

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a+2b = 3

ab = -5

2ab = -5×2

a(2b) = -10

we know the formula :

(x+y)³ = x³+y³+3xy(x+y)

(a+2b)³ = a³+(2b)³+3(a)(2b)(a+2b)

3³ = a³+8b³+3(-10)(3)

9 = a³+8b³-90

a³+8b³ = 9+90

a³+8b³ = 99

Hope it helps u :-)

Answer 2

a+2b=3
so a=3-2b
sustitute value of a in ab=-5
(3-2b)b=-5
3b-2b^2=-5
so   2b^2-3b-5
      Splitting the middle term
      2b^2+2b-5b-5
      2b(b+1)-5(b+1)
      (2b-5)(b+1)
      so b=5/2    and b=-1
     so a=-2       and a=5
so when b=5/2 and a=-2
so a^3+8b^3
    -8+125=117
  when b=-1      and a=5
so a^3+8b^3
    125-8=117
 so 117 is answer 
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