if x+y=13,xy=40,find the value of x³+y³
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Step-by-step explanation: x³ + y³ = (x + y)(x² - xy + y²)
We know the values of (x + y) and (xy) However we do not know the value of x² + y², so lets find out.
x +y = 13
we will start by squaring both sides
(x + y)² = (13)²
x² + xy + y² = 169
we know that xy = 40
x² + y² +40 = 169
x² + y² = 169 - 40
x² + y² = 129
Now we can find x³ + y³ as:
(x² + y²)(x² - xy + y²)
we know that x² + y² = 129 and x +y = 13 we also know that xy = 40
(129)(129 - 40)
(129)(89)
= 11481
=therfore x³ + y³ = 11481
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