Question 129

If $$x (x - 3) = - 1$$, than the value of $$x^{3} (x^{3} - 18)$$ is

Solution

$$x (x - 3) = - 1$$ eq-(1)
Cubing both the sides
($$(x)^{3}$$)($$(x)^{3}-27+27x-9(x)^{2}$$)= -1 eq(2)
From eq-(1) $$(x)^{2}-3x$$=-1
$$(x)^{2}-3x+1$$ = 0
or $$9(x)^{2}-27x+9$$ = 0
substituting above in equation 2 we get
$$x^{3} (x^{3} - 18)$$=-1


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