Question

If a+2b=3 and ab = -5 tgen find the value of 1. a^2 + 4b ^2 and 2. a^3+8b^3

Answer 1

Answer:

a² + 4b² = 29

a³ + 8b³ = 72

Step-by-step explanation:

1)

we given that

      a + 2b = 3

Taking square on both sides we get

 (a + 2b)² = 3²

using formula

    (a + b)² = a² + 2ab + b²

we get

a² + 2(a)(2b) + (2b)² = 9

⇒     a² + 4b² + 4ab = 9

⇒               a² + 4b² = 9 - 4ab

putting ab = -5 we get

                 a² + 4b² = 9 - 4(-5)

⇒              a² + 4b² = 9 + 20

⇒              a² + 4b² = 29

So

                 a² + 4b² = 29

2)

we given that

                  a + 2b = 3

Taking cube on both sides we get

                (a + 2b)³ = 3³

Using formula we get

       (a + b)³ = a³ + b³ + 3ab(a + b)

we get

      a³ + (2b)³ + 3a(2b)(a + 2b) = 27

 ⇒       a³ + (2b)³ + 6ab(a + 2b) = 27

Putting ab = -5 and (a + 2b) = 3 we get

               a³ + 8b³ + 6(-5)(3) = 27

⇒                    a³ + 8b³ - 90 = 27

⇒                            a³ + 8b³ = 27 + 90

⇒                            a³ + 8b³ = 117

So

                              a³ + 8b³ = 117