Question 55

If $$2x + y = 6$$ and $$xy = 4$$, then find the value of $$8x^3 + y^3$$ is:

Solution

Given, $$2x + y = 6$$ and $$xy = 4$$

$$=$$> $$\left(2x+y\right)^3=6^3$$

$$=$$> $$8x^3+y^3+3.2x.y\left(2x+y\right)=216$$

$$=$$> $$8x^3+y^3+6xy\left(2x+y\right)=216$$

$$=$$> $$8x^3+y^3+6\left(4\right)\left(6\right)=216$$

$$=$$> $$8x^3+y^3+144=216$$

$$=$$> $$8x^3+y^3=72$$

Hence, the correct answer is Option C

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