Question

Hi.....

The difference of two square nos. is 180 and the square of the smaller no. is 8 times the larger no. Find the two nos.

!!50 pts!!

Thanks!

Answer 1

Final Answer : Larger Number = 18
Smaller Number = ±12

Let the smaller number be 'y'and larger number be 'x'.

According to the question, we know
${x}^{2} - {y}^{2} = 180 \: \: \: \: \: \: \: \: \: \: \: - (1) \\ {y}^{2} = 8x \: \: \: \: \: \: \: \: \: \: - - - (2)$


Using eq. (1) and (2),

We get
${x}^{2} - 8x - 180 = 0 \\ = > {x}^{2} - 18x + 10x - 180 = 0 \\ = > x(x - 18) + 10(x - 18) = 0 \\ = > (x + 10)(x - 18) = 0 \\ = > x = 18or \: x = - 10(rejected)$
Since, x can't be negative as y^2 is always positive so 8x has to be positive.
=> x is positive.
x = -10 is rejected.


Now, substitute value of x = 18 in equation (2),
we get
y^2 = 8*18
=> y^2 = 144
=> y = ±12

Therefore, Larger number = 18
Smaller Number = 12 or -12

Answer 2

Answer:

!!

Step-by-step explanation:

Let the larger number = x

Then the square of the smaller number = 8 times the larger number = 8x

and the square of the larger number = x2

According to the question,

 x2 - 8x = 180

 =>  x2 - 8x - 180 = 0

 =>  x2 - 18x + 10x - 180 = 0

 =>  x(x - 18) + 10(x - 18) = 0

 =>  (x - 18) (x + 10)  = 0

 =>  x - 18 = 0  or x + 10 = 0

 =>  x = 18  or x = -10

Thus, the larger number = 18 or -10

Then, the square of the smaller number  = 8(18)  or     8(-10)

 = 144       or     -80

The square of a number can't be negative, so, the square of smaller number = 144

Hence, the smaller number = sqrt(144) = 12

The numbers are 12 and 18