Q. The no. of distinct pairs of (a, b) real numbers that would satisfy $\displaystyle x=x^3+y^4$and $\displaystyle y=2xy$.

A-5

B-12

C-3

D-7

dont laugh anyone on such elementary question....help!!

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- Oct 27th 2009, 10:03 PMfindmehere.geniusNeeding help in this question
Q. The no. of distinct pairs of (a, b) real numbers that would satisfy $\displaystyle x=x^3+y^4$and $\displaystyle y=2xy$.

A-5

B-12

C-3

D-7

dont laugh anyone on such elementary question....help!! - Oct 28th 2009, 01:33 AMearboth
I've found 5 pairs of real numbers (and 2 pairs of complex numbers).

$\displaystyle \left|\begin{array}{rcl}x&=&x^3+y^4 \\y&=&2 x y\end{array}\right.$ $\displaystyle \implies$ $\displaystyle \left|\begin{array}{rcl}x(1-x^2)-y^4&=&0 \\y(1-2x)&=&0\end{array}\right.$

All results containing y = 0 satisfy the second equation. From the first equation you'll get 3 different values of x if y = 0.

From the second equation you find out that $\displaystyle x = \frac12$ must be a possible x-value. Plug in this value into the first equation and calculate the corresponding y-values. - Oct 28th 2009, 02:26 AMfindmehere.genius
Thanks for the answer...now some paperwork needed to get them into head.