Question

If the sum of two number is 11, and the second number is greater by 3. Find the product of two number

Answer 1

Let the numbers be x and y.

According to the question,

x+y =11 —————(i)

1/x+1/y=11/3 ———(ii)

Simplifying (ii), we get( x+y)/xy=11/3 ——(iii)

Compare (i) with (iii) and it is evident that

xy =3

Or y = 3/x————-(iv)

Putting the value (y=3/x) in (i), we get

x^2–11x+3=0

It is a quadratic equation. Let us solve its two roots.

[ X={ -B +/-✔(B^2 - 4*A*C)}/2A]

x={-(-11) +/-✔(121–4*1*3)}/2

Or x= (11+✔109 )/2 or

x=(11 - ✔109 )/2

Therefore the two numbers are :—

i) (11 + ✔109)/2 and

(11 - ✔109 )/2

CHECK

(11+✔109 )/2 +( 11 - ✔109)/2=(11+11)2=11 OK

2 / (11+✔109 )+2/ (11-✔109)=

{2*(11-✔109 ) +2*(11+✔109}

_______________________________(divided by)

(11+✔109)*(11-✔109)

Or (22 -2✔109 +22+2✔109) /11+✔109)*(11-✔109)

Or =44/(11)^2 -(✔109)^2

{ (a+b)(a-b) =a^2 -b^2) FORMULA applied }

=44/(121–109)= 44/12=11/3 OK

Therefore the Greater Number is (11+✔109)/2