Question 67

If $$(x + 7)^3 + (2x + 8)^3 + (2x + 3)^3 = 3 (x + 7) (2x + 8) (2x + 3)$$, then what is the value of $$x$$ ?

Solution

Given, $$(x+7)^3+(2x+8)^3+(2x+3)^3 = 3(x+7)(2x+8)(2x+3)$$

$$=$$> $$(x+7)^3+(2x+8)^3+(2x+3)^3-3(x+7)(2x+8)(2x+3)=0$$

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

$$=$$> $$\left(x+7\right)+\left(2x+8\right)+\left(2x+3\right)=0$$

$$=$$> $$5x+18=0$$

$$=$$> $$x=\frac{-18}{5}$$

$$=$$> $$x=-3.6$$

Hence, the correct option is Option B

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