Question

Pls ans this qstion
if a+b= 4ab =3 then the value of a^(5)+b^(5) is equal to

Answer 1

Answer:

(a+b)^2= a^2+b^2+2ab

Putting the value of a+b and ab we get,

a^2+b^2=25–6

a^2+b^2=19 *

Now,

(a-b)^2= a^2+b^2–2ab

Putting the value of a^2+b^2=19

We get, (a-b)^2=19–6

a-b= √13, -√13

Answer 2

Answer:

The answer is $a^{5} +b^{5} = 150.1875$.

Step-by-step explanation:

Given that a + b = 3 and 4ab = 3

We have to find the value of $a^{5} +b^{5}$.

4ab = 3

ab = 3/4

a +b = 3

(a + b)² = 3²

⇒a² +b²+2ab = 9

⇒a²+b²+2(3/4) = 9

⇒a²+b²= 9-(3/2) =9-1.5 = 7.5

a² + b² = 7.5

(a² + b²)(a + b) = 7.5 × 3 = 22.5

⇒a³+b³+a²b+b²a = 22.5

⇒a³+b³+ab(a + b) = 22.5

⇒a³ + b³+(3/4)(3) = 22.5

⇒a³ + b³ = 22.5 - 9/4 = 22.5 - 2.25 = 20.25

(a³ + b³)(a² + b²) = (20.25)(7.5)

⇒$a^{5} +b^{5}+a^{3} b^{2} +a^{2} b^{3} = 151.875$

⇒$a^{5} +b^{5} +a^{2} b^{2} (a+b) = 151.875$

⇒$a^{5} +b^{5} +3(ab)^{2} = 151.875$

⇒$a^{5} +b^{5} = 151.875 - 3(\frac{3}{4})^{2} = 151.875 -\frac{27}{16} = 151.875 - 1.6875$

⇒$a^{5} +b^{5} = 150.1875$.

Therefore, $a^{5} +b^{5} = 150.1875$.