How 9 Cheenta students ranked in top 100 in ISI and CMI Entrances?

# Understand the problem

[/et_pb_text][et_pb_text _builder_version="3.23.3" text_font="Raleway||||||||" background_color="#f4f4f4" box_shadow_style="preset2" custom_margin="10px||10px" custom_padding="10px|20px|10px|20px"]Consider the two curves $y=2x^3+6x+1$ and $y=-3/x^2$ in the Cartesian plane. Find the number of distinct points at which these two curves intersect.

[/et_pb_text][/et_pb_column][/et_pb_row][et_pb_row _builder_version="3.22.4"][et_pb_column type="4_4" _builder_version="3.22.4"][et_pb_accordion open_toggle_text_color="#0c71c3" _builder_version="3.22.4" toggle_font="||||||||" body_font="Raleway||||||||" text_orientation="center" custom_margin="10px||10px"][et_pb_accordion_item title="Source of the problem" open="on" _builder_version="3.23.3" title_text_shadow_horizontal_length="0em" title_text_shadow_vertical_length="0em" title_text_shadow_blur_strength="0em" closed_title_text_shadow_horizontal_length="0em" closed_title_text_shadow_vertical_length="0em" closed_title_text_shadow_blur_strength="0em"]

#### Singapore Math Olympiad 2006 (Senior Section - Problem 23)

[/et_pb_text][et_pb_tabs active_tab_background_color="#0c71c3" inactive_tab_background_color="#000000" _builder_version="3.23.3" tab_text_color="#ffffff" tab_font="||||||||" background_color="#ffffff" custom_padding="|||22px||"][et_pb_tab title="Hint 0" _builder_version="3.22.4"]Do you really need a hint? Try it first!

[/et_pb_tab][et_pb_tab title="Hint 1" _builder_version="3.23.3"]Try to think how to find the intersection points using these two given equation $y=2x^3+6x+1$ and $y=-3/x^{2}$

[/et_pb_tab][et_pb_tab title="Hint 2" _builder_version="3.23.3"]Try to compare the two values of y e.g.$2x^3+6x+1=-3/x^{2}$ Do we get two factors $2x^3+1=0$ and $x^2+3=0$

[/et_pb_tab][et_pb_tab title="Hint 3" _builder_version="3.23.3"]

At end as we will consider only $2x^3+1=0$ as $x^2+3>0$

[/et_pb_tab][et_pb_tab title="Hint 4" _builder_version="3.23.3"]

Thus we will get the value of x and from there we can find the value of y and we will get the answer.  $(\frac{-1}{\sqrt [3]{2}}, \frac{-3}{\sqrt [3]{4}})$

So the number distinct point will be 1

# Similar Problems

[/et_pb_text][et_pb_post_slider include_categories="9" _builder_version="3.22.4"][/et_pb_post_slider][et_pb_divider _builder_version="3.22.4" background_color="#0c71c3"][/et_pb_divider][/et_pb_column][/et_pb_row][/et_pb_section]

# Knowledge Partner

Cheenta is a knowledge partner of Aditya Birla Education Academy