Question

if 460 is divided by a natural number quetient is 6 more than five times the divisor &remainder is 1. find quotient &division

Answer 1

By the Equation,

Divident=Divisor ×Quotient+remainder.

→460=Divisor×[(5divisor)+6]+1
Let divisor Be D

→460-1=D[5D+6]
→459=5D²+6D

→5D²+6D-459=0

So b²-4ac =36-(-9180)
=9216.

HereD=[-(6)±√9216]÷[2×5]
→D=[-6±96]÷10

So D =(-6+96)/10=90/10=9.

Or D=(-6-96)/10=(-102)/10=(-10.2)

So Divisor is 9 or -10.2

When Divisor is 9
Quotient=5(9)+6=45+6=51.

And When Divisor is -10.2

Quotient=5(-10.2)+6=-51+6=(-45).

Hope it Helps...
Regards,
Leukonov.