If (135√5x2 - 2√2y3) ÷ (3√5x - √2y) = Ax2 + By2 + $$\sqrt {10} $$ Cxy, then the value of (A + B - 9C) is:
A. 18
B. 12
C. 20
D. 10
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & \left( {135\sqrt 5 {x^3} - 2\sqrt 2 {y^3}} \right) \div \left( {3\sqrt 5 x - \sqrt 2 y} \right) = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & \Rightarrow \frac{{{{\left( {3\sqrt 5 x} \right)}^3} - {{\left( {\sqrt 2 y} \right)}^3}}}{{3\sqrt 5 x - \sqrt 2 y}} = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & \Rightarrow \frac{{\left( {3\sqrt 5 x - \sqrt 2 y} \right)\left( {45{x^2} + 2{y^2} + 3\sqrt {10} xy} \right)}}{{\left( {3\sqrt 5 x - \sqrt 2 y} \right)}} = A{x^2} + B{y^2} + \sqrt {10} Cxy \cr & {\text{Comparison both side,}} \cr & A = 45,\,B = 2,\,C = 3 \cr & A + B - 9C = \left( {45 + 2 - 27} \right) \cr & A + B - 9C = 20 \cr} $$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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