Question

X*3 -y*3=117/8, x-y=3/2,. X*2+xy+y*2=

Answer 1

Answer:

39

x²+xy+y²=-------

4

Step-by-step explanation:

Given--->

-----------

x³-y³=117/8 , x-y=3/2

To find---> x²+xy+y²=?

------------

Solution---->We know that

------------- (x-y)³=x³-y³-3xy(x-y)

=> (x-y)³+3xy(x-y)=x³-y³

=> x³-y³=(x-y)³+3xy(x-y)

Taking (x-y)common from RHS

=>x³-y³=(x-y){(x-y)²+3xy}

=>x³-y³=(x-y) (x²+y²-2xy+3xy)

=>x³-y³=(x-y) (x²+y²+xy)

Now putting x³-y³=117/8 and x-y=3/2

=>117/8=(3/2) (x²+y²+xy)

117 2 39

=>x²+y²+xy=---------× ------- = ---------

8 3 4

Additional information--->

------------------------------------

1)(a+b)³=a³+b³+3ab(a+b)

2)a³+b³=(a+b)(a²+b²-ab)

3)a³+b³+c³-3abc=(a+b+c)(a²+b²+c²-ab-

bc-ca)

4)If a+b+c=0

a³+b³+c³-3abc=0