urgent help please... solving simultaneous with powers.

• Dec 16th 2009, 03:56 PM
vivien
urgent help please... solving simultaneous with powers.
If x^2 + y^2 =58 and xy=21, find the vlaue of (x+y)^2 and (x-y)^2.

if x^2+y^2=1 and xy = 7.5 , find the value of (x^4 -y^4)

i really don't know how to start , have been thinking for the whole night, still can't do it :(

Thank you.
• Dec 16th 2009, 04:01 PM
skeeter
Quote:

Originally Posted by vivien
If x^2 + y^2 =58 and xy=21, find the vlaue of (x+y)^2 and (x-y)^2.

$\textcolor{red}{(x+y)^2 = x^2+2xy+y^2 = (x^2+y^2)+2xy = 58 + 2(21) = 100}$

get the idea?

if x^2+y^2=1 and xy = 7.5 , find the value of (x^4 -y^4)

i really don't know how to start , have been thinking for the whole night, still can't do it :(

Thank you.

...
• Dec 16th 2009, 04:04 PM
pickslides
Quote:

Originally Posted by vivien
If x^2 + y^2 =58 and xy=21, find the vlaue of (x+y)^2 and (x-y)^2.

$x^2 + y^2 =58$ ....(1)

$xy=21$ ....(2)

From (2) you can say $y = \frac{21}{x}$ and sub this back into (1) giving

$x^2 + \left(\frac{21}{x}\right)^2 =58$ ....(1)

Now solve for x

I think skeeter's way could be better.