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OpenStudy (aonz):
If x + y = 1 and x^3 + x^3 = 19 find value of x^2 + y^2
OpenStudy (anonymous):
x^3 + x^3 = 19 ?
2x^3 = 19
x^3 = 19/2
x = cubed root of 19/2
u can substitute this into the first equation x + y = 1 to solve for y, then you can solve for x^2 + y^2
OpenStudy (aonz):
opps i meant x^3 + y^3 =19
OpenStudy (anonymous):
i thought thats what u meant thats why i put a ? after it :)
OpenStudy (aonz):
yes
(a + b)(a^2 - ab + b^2)
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OpenStudy (anonymous):
Great :)
a³ + b³ = (a + b)(a² - ab + b²)
19 = 1 (a² - ab + b²)
OpenStudy (aonz):
umm ok... i still dont think i get the question
OpenStudy (anonymous):
i would just use substitution
OpenStudy (aonz):
how :P
OpenStudy (anonymous):
let y = 1 - x
then y^3 = (1 - x)^3
expand it out
then you can write x^3 + (1 - x)^3 = 19
should come out nicely
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OpenStudy (anonymous):
a² + b² - ab = (a + b)² - 2ab -ab
19 = 1 - 3ab
-> ab = -18/ 3 = -6