If 2x - y = 2 and xy = $$\frac{3}{2},$$ then what is the value of $${x^3} - \frac{{{y^3}}}{8}?$$
A. $$\frac{{13}}{4}$$
B. $$\frac{9}{2}$$
C. $$ - \frac{5}{4}$$
D. $$\frac{5}{2}$$
Answer: Option A
Solution(By Examveda Team)
$$\eqalign{ & 2x - y = 2{\text{ and }}xy = \frac{3}{2} \cr & 2x - y = 2 \cr & {\text{divide '2' both sides}} \cr & x - \frac{y}{2} = 1 \cr & {\text{cube both sides}} \cr & {\left( {x - \frac{y}{2}} \right)^3} = {1^3} \cr & {x^3} - \frac{{{y^3}}}{8} - 3 \times x \times \frac{y}{2}\left( {x - \frac{y}{2}} \right) = {1^3} \cr & {x^3} - \frac{{{y^3}}}{8} = {1^3} + 3 \times \frac{3}{2} \times \frac{1}{2} \times 1 \cr & {x^3} - \frac{{{y^3}}}{8} = 1 + \frac{9}{4} \cr & {x^3} - \frac{{{y^3}}}{8} = \frac{{13}}{4} \cr} $$Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
B. x + 4
C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
A. $$\frac{{20}}{{27}}$$
B. $$\frac{{27}}{{20}}$$
C. $$\frac{6}{8}$$
D. $$\frac{8}{6}$$
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