Question

146) If the sum of 2 numbers is 1 and their product is 1, then what is the sum of their cubes?

Answer 1

Given that the sum of 2 numbers is 1 and their product is 1, let's find the sum of their cubes.

Let x and y represent the numbers.

Thus, we have:

x + y = 1..........................equation 1

x y = 1...........................equation 2

Here, we are to find x³ + y³ .

Thus, we can write this as:

$x^3+y^3=(x+y)(x^2+y^2-xy)$

Manipulating this, we can write:

$x^3+y^3=(x+y)((x+y)^2-3xy))$

Substitute the values for x+y and xy into the equation above, we have:

$\begin{gathered} x^3+y^3=(1)((1)^2-3(1)) \\ \\ x^3+y^3=(1)(1-3) \\ \\ x^3+y^3=-2 \end{gathered}$

Therefore, the sum of their cubes is -2.

ANSWER:

-2