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Question

Solve the following equations:
3x24x+3x24x6=18.

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Solution

3x24x+3x24x6=183x24x6+3x24x6=12(3x24x6)2+3x24x6=12
Put 3x24x6=t
t2+t=12t2+t12=0t2+4t3t12=0t(t+4)3(t+4)(t3)(t+4)=0t=3,43x24x6=t3x24x6=t23x24x6=323x24x15=0.....(i)
Also, 3x24x6=(4)2
3x24x22=0........(ii)
Solving (i)
3x24x15=03x29x+5x15=03x(x3)+5(x3)=0(3x+5)(x3)=0x=53,3
Solving (ii)
3x24x22=0
Using quadratic formula
x=4±164(3)(22)2(3)=4±2806x=4±2706=2±703
So the values of x are 2+703,2703,53 and 3

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