If 5√5x3 + 2√2y3 = (Ax + √2y)(Bx2 + 2y2 + Cxy), then the value of (A2 + B2 - C2) is:
A. 15
B. 20
C. 40
D. 30
Answer: Option B
Solution(By Examveda Team)
$$\eqalign{ & 5\sqrt 5 {x^3} + 2\sqrt 2 {y^3} = \left( {Ax + \sqrt 2 y} \right)\left( {B{x^2} + 2{y^2} + Cxy} \right) \cr & {\left( {\sqrt 5 x} \right)^3} + {\left( {\sqrt 2 y} \right)^3} = \left( {\sqrt 5 x + \sqrt 3 y} \right)\left( {5{x^2} + 9{y^2} - \sqrt {10} xy} \right) \cr & \left( {\sqrt 5 x + \sqrt 3 y} \right)\left( {5{x^2} + 9{y^2} - \sqrt {10} xy} \right) = \left( {Ax + \sqrt 2 y} \right)\left( {B{x^2} + 2{y^2} + Cxy} \right) \cr & {\text{Comparison both side:}} \cr & A = \sqrt 5 \cr & B = 5 \cr & C = - \sqrt {10} \cr & {A^2} + {B^2} + {C^2} = 5 + 25 - 10 = 20 \cr} $$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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