Question

please sove the problem given below

Answer 1

Hey mate here's ur answer :-)

1) Let numerator be x and denominator be y

Given that: y = 3 + x and x/y + y/x = 29/10

x/y + y/x = 29/10

x2 + y2 / xy = 29/10

x2 + 9 + x2 + 6x / 3x + x2 = 29/10

2x2+ 6x + 9 / x2+ 3x = 29/10

9x2+ 27x - 90 = 0

x2+ 3x - 10 = 0

x = 2

y = 3+2 = 5

Therefore fraction = x/y = 2/5

2)

let the numerator be 'x' then denominator is'2x+1'

given="x / 2x+1" + "2x+1/x"=2 16/21

then="x / 2x+1" + "2x+1/x"=58/21

=x(x)+2x+1(2x+1) / 2x+1(x=58/21

=x2+(2x+1)2  / 2x2+x=58/21

=x2+4x2+4x+1 / 2x2+x=58/21

=5x2 +4x+1 / 2x2+x=58/21

=5x2 +4x+1(21)=58(2x2+x)

=105x2 +84x+21=116x2 +58x

=116x2 +58x-105x2 -84x-21=0

=11x2 - 26x-21=0

by solving using x= -(b)+rootb2 -4ac /2a

we get x=3 so the fraction is 3/7

check

3/7 +7/3 =49 +9 /21=58 /21

hence verified

hope it helps...