Question

ii) The difference between squares of two num.
bers is 12
0 The square 120. The square
of the smaller number is twice the greater
number. Find the numbers​

Answer 1

Answer: Hope this helps you...

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 a smaller number is twice the larger number, therefore the square of any number cant be negative,

Thus x cant take a 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

Answer 2

Answer:

Let the greater no. Be X and the other no be y

y²=2x

case.i

x²-y²=x²-2x=120

x²-2x-120=0

x²+10x-12x-120=0

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

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

x-12=0 ,x=12

x+10=0

x=-10

the number can't be negative, so x=12

the small no is y²=2×12

y=2√6

thus the number are 12 and 2√6