Question

If X+Y=4, 1/X + 1/Y =16/15,then find the value of X^3 + Y^3 = ?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given,

First equation is :

X+Y = 4

Second equation is :

(1/X) + (1/Y) = 16/15

To find,

Value of (X³+Y³)

Solution,

We can simply solve this mathematical problem by using the following mathematical process.

Here, we have to use normal algebraic method.

Now, from second given equation, we get -

(1/X) + (1/Y) = 16/15

or, (Y+X)/XY = 16/15

or, (X+Y)/XY = 16/15

or, 4/XY = 16/15 (putting the given value of X+Y)

or, 16 × XY = 4×15

or, 16 × XY = 60

or, XY = 60/16

or, XY = 3.75

Now, finding the value of (X³+Y³) :

From, the formula of :

(a+b)³ = a³+b³+3ab(a+b)

We can write that,

(X+Y)³ = X³+Y³+3XY(X+Y)

or, (4)³ = X³+Y³+(3×3.75×4)

or, 64 = X³+Y³+45

or, X³+Y³ = 64-45

or, X³+Y³ = 19

(This will be considered as the final result.)

Hence, value of (X³+Y³) is 19