Problem: The value of xxx at the intersection of y=8x2+4y=\dfrac{8}{x^{2}+4}y=x2+48 and x+y=2x+y=2x+y=2 is
Answer Choices:
A. −2+5-2+\sqrt{5}−2+5
B. −2−5-2-\sqrt{5}−2−5
C. 000
D. 222
E. none of these Solution:
For intersection 8/(x2+4)=2−x8 /\left(x^{2}+4\right)=2-x8/(x2+4)=2−x.
∴x3−2x2+4x=x(x2−2x+4)=0;∴x=0.\therefore x^{3}-2 x^{2}+4 x=x\left(x^{2}-2 x+4\right)=0 ; \quad \therefore x=0 . ∴x3−2x2+4x=x(x2−2x+4)=0;∴x=0.