Question

pls solve this and tell me with steps

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Answer 1

Answer:

(x^9999 + x^8888 + x^7777 + ..... + x^1111 + 1)/(x^9+x^8+x^7+.....+x^1)

=x^1111[(x^9+x^8+x^7+....+x^1+1)/(x^9+x^8+x^7+....+x^1 +1)]

= x^1111(1)

=x^1111

hence proved...

hey sorry... but don't take this ans. because this is wrong ans... sorry for my mistake... :(

Answer 2

Consider P-Q=x^9999+......x^1111+1-x^9.....1

=x^9999-x^9+x^8888-x^8+.....+x^1111-x

=x^9((x^9990)-1)+x^8((x^8880)-1)+.....x((x^1110)-1)

=x^9[((x^10)^999)-1]+x^8[((x^10)^888)-1]+.....x[((x^10)^

111)-1]

Observe ((x^10)^n)-1 is divisible by( x^10)-1 for all

n>=1

So P-Q is divisible by (x^10)-1........(1)

And( x^10)-1 =(x-10)(x^9+x^8+x^7.....(1)

or x^9+x^8.....+1 divides (x^10)-1

or Q divides (x^10)-1 or Q divides P-Q (using 1)

So Q DIVIDES P

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