Question

Evaluate: (4.56 ^3 + 5.44^3) / (4.56^2 - 4.56 * 5.44 + 5.44^2)

Answer 1

Answer:10

Step-by-step explanation:

Answer 2

Answer:

The correct answer for the given expression is found to be 10.

Step-by-step explanation:

We are given the expression as follows:

$=\frac{(4.56)^3+(5.44)^3}{(4.56)^2+(5.44)^2-(5.44)(4.56)}$

Now, we know the identity of sum of cubes of two real numbers that is as follows:

$a^3+b^3=(a+b)(a^2-ab+b^2)$

Modifying this identity, we get:

$\frac{a^3+b^3}{(a^2-ab+b^2)}=a+b$                          ...(i)

Observing the given problem and comparing it with the above identity, we can see that the given problem is of the form of L.H.S. of (i), where

a = 4.56 and b = 5.44

Substituting a and b now in (i), we get:

$\frac{(4.56)^3+(5.44)^3}{(5.44)^2-(4.56)(5.44)+(4.56)^2)}=4.56+5.44$

Simplifying the R.H.S., we get:

$\frac{(4.56)^3+(5.44)^3}{(5.44)^2-(4.56)(5.44)+(4.56)^2)}=10$

Thus, the correct answer for the given expression is found to be 10.