Question

if 5√5x^3 +2√y^3 =(Ax+√2y) (Bx^2+2y^2+Cxy) than find the value of A^2 +B^2-C^2

Answer 1

Required numeric value of 6A + B - √15 C is 12.

Step-by-step explanation:

Given,

( 5√5 x^3 - 81√3 y^3 ) ÷ ( √5 x - 3√3 y ) = Ax^2 + By^2 + Cxy

Simplifying Left Hand Side

= > ( 5√5 x^3 - 81√3 y^3 ) ÷ ( √5 x - 3√3 y )

= > [ ( √5 x )^3 - ( 3√3 y )^3 ] ÷ [ √5 x - 3√3 y ]

From the properties of expansion :

a^3 - b^3 = ( a - b )( a^2 + ab + b^2 )

= > [ ( √5 x - 3√3 y ){ ( √5 x )^2 + ( √5 x × 3√3 y ) + ( 3√3 y )^2 ] ÷ ( √5 x - 3√3 y )

= > ( √5 x )^2 + ( √5 x × 3√3 y ) + ( 3√3 y )^2

= > 5x^2 + 3√15 xy + 27y^2

On comparing left hand side with the right hand side :

= > 5 = A, since both have same coefficient.

= > 3√15 = C, since both have same coefficient

= > 27 = B, since both have same coefficient.

Thus,

= > 6A + B - √15 C

= > 6( 5 ) + 27 - √15 ( 3√15 )

= > 30 + 27 - 3( √15 × √15 )

= > 57 - 3( 15 )

= > 57 - 45

= > 12

Hence the required numeric value of 6A + B - √15 C is 12......