Question

the difference between squares of two numbers is 120 . the square of smaller number is twice the greater number. find the numbers.

Answer 1

The difference between squares of two numbers is 120 . the square of smaller number is twice the greater number. find the numbers

let smaller number be x and bigger be y

ACQ,

y² = 2x

and

x²  - y²  = 100

since y² = 2x

so

x^2 - 2x = 120

x^2 - 2x - 120 = 0

x^2 - 12x + 10x - 120 = 0

x(x -12) +10(x - 12) = 0

(x-12)(x+10) = 0

so

x = 12/-10

but it can be -10 because   the square of smaller number is twice the larger number, therefore the square of any number cant be negative

so,

2x = 2 *12

= 24

y² = 24

y = √24

y = 2√6

hence the numbers are 12 and 2√6
:)

Answer 2

Let the greater no be x and smaller no be y
So A. To. Q
x²-y²=120--------------(1)
Also
y²=2x
Put y²=2x in eq (1)
x²-2x=120
2x²-2x-120=0
x²-12x+10x-120=0
x(x-12)+10(x-12)=0
(x-12)(x+10)=0
x=12 and x=-10
$so \: y = 2 \sqrt{6} \: \: \: and \: \: y = \sqrt{ - 20}$
Buy second result is imagenary hence ans is 12 and 2root6