Question 328149
{{{x^4-2x^3-17x^2+4=-3x^4-2x^3+20x^2-5}}}
{{{4x^4-37x^2+9=0}}}
Use a substitution.
Let {{{u=x^2}}}, {{{u^2=x^4}}}
{{{4u^2-37u+9=0}}}
{{{(4u-1)(u-9)=0}}}
Two solutions in u:
{{{ 4u-1=0}}}
{{{ 4u=1}}}
{{{ u=1/4}}}
{{{ x^2=1/4}}}
{{{ highlight_green(x=0 +- 1/2)}}}
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{{{u-9=0}}}
{{{u=9}}}
{{{x^2=9}}}
{{{highlight_green(x=0 +- 3)}}}
Solve for y with each x using either equation.
{{{highlight( x=1/2)}}},{{{y=(1/2)^4-2(1/2)^3-17(1/2)^2+4=1/16-1/4-17/4+4=-7/16}}}
{{{highlight(y=-7/16)}}}
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{{{highlight( x=-1/2)}}},{{{y=(1/2)^4+2(1/2)^3-17(1/2)^2+4=1/16+1/4-17/4+4=1/16}}}
{{{highlight(y=1/16)}}}
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{{{highlight( x=3)}}},{{{y=3^4-2(3)^3-17(3)^2+4=81-54-153+4=-122}}}
{{{highlight(y=-122)}}}
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{{{highlight( x=-3)}}},{{{y=3^4+2(3)^3-17(3)^2+4=81+54-153+4=-14}}}
{{{highlight(y=-14)}}}