Question

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

Answer 1

hey buddy!!

Here is your answer;

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⭐⭐⤵

Let the numbers be x and y where x>y so,

x^2 - y^2 = 120.....(1)

y^2 = 2 x.....(2)

Putting (2) in (1), we get

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 can be 12 or -10, but we are given that the square of smaller number is twice the larger number, therefore the square of any number cant be negative,

Thus x cant take value of -10

So x = 12, so y^2 = 2 (12)

y^2 = 24

So y = √24 or - √24

y = 2√6 or -2√6

Hence the numbers are 12 and 2√6 or 12 and -2√6

➡hope this helps you deaR ✌✌✌.

Answer 2

${Answer :-}$

Let, one number be x and the other be y, where x > y.
So, x^2 - y^2 = 120............ (1)

Again, the square of the smaller number is the twice the greater number.
So, y^2 = 2x........... (2)

From (1) and (2),
x^2 - y^2 = 120.
Or, x^2 - 2x = 120.
Or, x^2 - 2x - 120 = 0.
Or, x^2 - 12x + 10x - 120 = 0.
Or, x(x-12) + 10(x-12) = 0.
Or, (x-12)(x+10) = 0.
Or, x = 12, (-10)

Now, if x = 12,
y = ( 2*12) ^1/2 = (24)^1/2
Or, y = root 24.

Now, if x = (-10)
y = (2 * - 10) ^1/2 = (-20)^1/2
Or, y = root (-20)

Root over of any negative integer is not defined.

Thus, x =12 and y = root 24.

Hope this helps,.

If helps, please mark it as brainliest ^_^