Reverse coefficients

Number Theory Level 4

If the coefficient of x a y b x^a y^b in ( x + 2 y ) ( x + 3 y ) ( x + 5 y ) ( x + 7 y ) ( x + 11 y ) ( x + 13 y ) . . . . . . . ( x + 71 y ) (x+2y)(x+3y)(x+5y)(x+7y)(x+11y)(x+13y).......(x+71y) is 639 Find b − a b-a


The answer is -18.

Alamuru Ganesh by Alamuru Ganesh , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

J Ravindranath
Feb 2, 2020

Take y common from all the terms y ( 20 ) ∗ ( ( x / y ) + 2 ) ∗ ( ( x / y ) + 3 ) ∗ . . . . . . . ( ( x / y ) + 71 ) y^(20)*((x/y)+2)*((x/y)+3)*.......((x/y)+71) = y ( 20 ) ∗ ( ( x / y ) ( 20 ) + 639 ∗ ( x / y ) ( 19 ) + − − − − − − − y^(20) * ((x/y)^(20) + 639*(x/y)^(19)+------- = x ( 20 ) ∗ y ( 20 ) + 639 ∗ x ( 19 ) ∗ y + − − − − − − − − − − x^(20)*y^(20) + 639*x^(19)*y+---------- a=19,b=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...