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If x+y=5 and xy=6 , then the value of x^...

If `x+y=5` and `xy=6` , then the value of `x^(3)+y^(3)` is

A

`35`

B

`45`

C

`30`

D

`125`

Text Solution

AI Generated Solution

The correct Answer is:
To find the value of \( x^3 + y^3 \) given that \( x + y = 5 \) and \( xy = 6 \), we can use the formula for the sum of cubes: \[ x^3 + y^3 = (x + y)^3 - 3xy(x + y) \] ### Step-by-step solution: 1. **Identify the values:** - We have \( x + y = 5 \) and \( xy = 6 \). 2. **Calculate \( (x + y)^3 \):** \[ (x + y)^3 = 5^3 = 125 \] 3. **Calculate \( 3xy(x + y) \):** \[ 3xy(x + y) = 3 \cdot 6 \cdot 5 = 90 \] 4. **Substitute into the formula:** \[ x^3 + y^3 = (x + y)^3 - 3xy(x + y) \] \[ x^3 + y^3 = 125 - 90 \] 5. **Calculate the final result:** \[ x^3 + y^3 = 35 \] Thus, the value of \( x^3 + y^3 \) is **35**.
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