The sum of two positive numbers is 5 times their difference. If sum of their squares is 208, then

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05 Jul 2010 Difference between numbers?

The sum of two positive numbers is 5 times their difference. If sum of their squares is 208, then the positive difference of
the numbers will be

OPtion

1) 9
2) 3
3) 2
4) 1
5) 6
6) 8
7) 4
8) 10
9) 12
10) 14

Solution

x+y = 5 (x-y) => x + y = 5x – 5y
=> 6y = 4x
=> x/y = 3/2
=> x = 3y/2 (i)
And x2 + y2 = 208 (ii)
On taking the value of x from eq. (i) in eq. (ii), we get
(3y/2)2 + y2 = 208
=> 2.25y2 + y2 = 208
=> y2 = 208/3.25 = 64
=> y = 8
x = 3y/2 = 12
Difference = 4

Correct Option: 7 Best Solution (16)

Pargat Pal Singh   14 years AGO

Nos are 12 and 8. diff is 4.

Like? Yes (1) | No   

Dolly   14 years AGO

(x+y)=5*(x-y)= 5x-5y or 4x=6y or x= 1.5 y
x^2+y^2= 208 or y^2+ (1.5y)^2 = 3.25Y^2=208......
or y^2=64 , then y=8 and x=12

x-y =4

Like? Yes (1) | No   

Dr.Dipin Singh   14 years AGO

x+y= 5*(x-y) and x^2+y^2=208, solvinf these eqns, we get , x=12 and y =8.

x-y=12-8=4.. option 7

Like? Yes (1) | No   

SUDESHNA SEN   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Mamon Sengupta   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Trishita Dasgupta   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Arneet   14 years AGO

When nos are 12 and 8,
20=5*4 and

12^2+8^2 =208, then

12-8=4.

Like? Yes (1) | No   

ASHOK ROY   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Sudeshna Sengupta   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Parbati Sen   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

Ashu   14 years AGO

12-8=4

Like? Yes (1) | No   

Somdatta Mukherjee   14 years AGO

Let the no.s be x and y.
Then x+y=5(x-y)
And x^2+y^2=208.
or, 2(x^2+y^2)= 416
or, (x+y)^2+(x-y)^2=416
or, 25(x-y)^2+(x-y)^2=416
or, 26(x-y)^2=416
or, (x-y)^2=16
or, x-y=4.....Option 7)

Like? Yes (1) | No   

meda visweswararao   14 years AGO

x+y=5(x-y)&x^2+y^2=208
then y=8,x=12

Like? Yes (1) | No   

Aman   14 years AGO

(12-8)*5= 12+8 and 12^2+8^2=208

so diff =12-8=4

Like? Yes (1) | No   

Inder Singh Negi   14 years AGO

simply calculate 3y=2x and put in second eq.

Like? Yes (1) | No   

leejia james   14 years AGO

let a,b be the nos
a+b=5(a-b) ie 3b=2a ie b=2a/3
a^2+b^2=208 ie a^2+(2a/3)^2=208
s0 a^2=144 b^2=64
a=12 b=8 so difference 4

Like? Yes (1) | No