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Question

Solve the following equations:
4x420x3+33x220x+4=0.

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Solution

Given equation, 4x420x3+33x220x+4=0

4(x2+x2)20(x+x1)+33=0[dividing byx2]

Substitute x+x1=y in the above equation

4(y22)20y+33=04y220y+25=0(2y5)2=0

We have equal roots for y=52

x+x1=522x25x+2=0(2x1)(x2)=0

roots of the given equation are 12,12,2,2


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