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