Random Maths Question - Year 11 Extension I (1 Viewer)

[phoenix159]

i) Factorise x³ + y³
ii) Hence find the value for x² + y² if:
x + y = 7
and
x³ + y³ = 19

for the first part I got: x³ + y³ = (x + y)(x² - xy + y²)

For the second part of the question I got 127/7 but i'm not sure if it's correct

Here is the working out:

(x + y)² = 7² = 49
(x + y)² = x² + y² + 2xy
(x² + y²) + 2xy = 49
7(x² + y²) + 14xy = 343 ... (1)

Using the expansion from above:
x³ + y³ = (x + y)(x² - xy + y²)

Subbing in the given values:
19 = 7 (x² - xy + y²)
38 = 14 (x² - xy + y²)
14(x² + y²) - 14xy = 28 ... (2)

(1) + (2) gives:

21(x² + y²) = 381
x² + y² = 381/21 = 127/7

Any help would be appreciated

 

[Sy123]

Yes you are correct, it is indeed 127/7