If (x+y)=13 and xy=36 then the value of `(x^3+y^3)` is:

Options

A. 369
B. 936
C. 693
D. none of these

Answer

To find the value of \( x^3 + y^3 \) given that \( x + y = 13 \) and \( xy = 36 \), we can use the identity:

\[ x^3 + y^3 = (x + y)^3 - 3xy(x + y) \]

### Step 1: Calculate \( (x + y)^3 \)

Given \( x + y = 13 \), we can calculate:

\[ (x + y)^3 = 13^3 \]

Calculating \( 13^3 \):

\[ 13^3 = 13 \times 13 \times 13 = 169 \times 13 = 2197 \]

### Step 2: Calculate \( 3xy(x + y) \)

Next, we need to calculate \( 3xy(x + y) \). We know \( xy = 36 \) and \( x + y = 13 \):

\[ 3xy(x + y) = 3 \times 36 \times 13 \]

Calculating \( 3 \times 36 \):

\[ 3 \times 36 = 108 \]

Now, multiply by \( 13 \):

\[ 108 \times 13 = 1404 \]

### Step 3: Substitute into the identity

Now we can substitute our results into the identity:

\[ x^3 + y^3 = (x + y)^3 - 3xy(x + y) = 2197 - 1404 \]

Calculating \( 2197 - 1404 \):

\[ 2197 - 1404 = 793 \]

### Final Answer

Thus, the value of \( x^3 + y^3 \) is:

\[ \boxed{793} \]

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