SOLUTION: Please help me figure this out. If x-y=9 and xy=3, then x^2+y^2=? Answers: a) 36 b) 2(sqrt of 21) c) sqrt of 87 d) 84 e) 87

Algebra ->  Formulas -> SOLUTION: Please help me figure this out. If x-y=9 and xy=3, then x^2+y^2=? Answers: a) 36 b) 2(sqrt of 21) c) sqrt of 87 d) 84 e) 87      Log On


   

Question 121551: Please help me figure this out.
If x-y=9 and xy=3, then x^2+y^2=?
Answers:
a) 36
b) 2(sqrt of 21)
c) sqrt of 87
d) 84
e) 87
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If x-y=9
and xy=3 solve this system to find x and y

+xy=3…..=>.y+=+3%2Fx…..=>.substitute into:
+x-y=9…….=>….
x-3%2Fx=9...both sides multiply by x
x%5E2-3=9x
x%5E2+-9x+-3=0 .....use quadratic formula to solve for x

x%5B1%2C2%5D=%28-b+%2B-+sqrt+%28b%5E2+-4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29
x%5B1%2C2%5D=%28-%28-9%29+%2B-+sqrt+%28%28-9%29%5E2+-4%2A1%2A%28-3%29+%29%29+%2F+%282%2A1%29
x%5B1%2C2%5D=%289+%2B-+sqrt+%2881+%2B+12+%29%29+%2F+2
x%5B1%2C2%5D=%289+%2B-+sqrt+%2893+%29%29+%2F+2
x%5B1%2C2%5D=%289+%2B-+9.64+%29+%2F+2
x%5B1%5D=%289+%2B+9.64+%29+%2F+2
x%5B1%5D=%2818.64+%29+%2F+2
+highlight+%28x%5B1%5D=+9.32%29+
x%5B2%5D=%289+-+9.64+%29+%2F+2
x%5B2%5D=%28-.64+%29+%2F+2
+highlight+%28x%5B2%5D=+-%28+.32%29%29

=>. y%5B1%5D+=+3%2Fx …
+y%5B1%5D+=+%283%2F9.32%29
highlight%28y%5B1%5D=+.32%29
=>. y+=+3%2Fx …..=>.
++y%5B2%5D+=+%283%2F-.32%29
highlight%28y%5B2%5D+=-9.375%29+


then
x%5E2%2By%5E2=+%289.32%29%5E2+%2B+%28.32%29%5E2=86.8624+%2B0.1024=86.9648+=+87...


x%5E2%2By%5E2=+%28-+.32%29%5E2+%2B+%28-9.375%29%5E2=+0.1024+%2B+87.890625=87.993025

so, your answer is:
e) 87