Question 63

If $$(x - 8)^3 + (2x + 16)^3 + (2x - 13)^3 = 3 (x - 8) (2x + 16) (2x - 13 )$$, then what is the value of $$x$$ ?

Solution

Given, $$(x-8)^3+(2x+16)^3+(2x-13)^3 = 3(x-8)(2x+16)(2x-13)$$

$$=$$> $$(x-8)^3+(2x+16)^3+(2x-13)^3-3(x-8)(2x+16)(2x-13)=0$$

We know that if $$a^3+b^3+c^3-3abc=0$$ then $$a+b+c=0$$

$$=$$> $$\left(x-8\right)+\left(2x+16\right)+\left(2x-13\right)=0$$

$$=$$> $$5x-5=0$$

$$=$$> $$x=\frac{5}{5}$$

$$=$$> $$x=1$$

Hence, the correct option is Option A

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