Question

The difference of squares of two numbers is 180. The square of the smaller number is 8

times the larger number. Find the two numbers.​

Answer 1

Answer:

The smaller number is $\pm12$ and the larger one is $18$.

Step-by-step explanation:

Let $x$ be the smaller number.

Then the larger number is $\frac18x^2$.

So

$\big(\frac18x^2\big)^2-x^2=180\\x^4-64x^2-11520=0\\(x-12)(x+12)(x^2+80)=0$

As $x$ is real, $x=\pm12$. So the larger number is $12^2\div8=18$.

Answer 2

Answer:

We have,

Let the large number is =x

Square of smaller number is =8x

Now, According to given question,

x2−8x=180

⇒x2−8x−180=0

⇒x2−(18−10)x−180=0

⇒x2−18x+10x−180=0

⇒x(x−18)+10(x−18)=0

⇒(x−18)(x+10)=0

⇒x−18=0,x+10=0

⇒x=18,x=−10

⇒x=−10,18

Either

x=−10 and x=18

x=18 is true (Positive value)

Now, square of small number

=18x=18×8=144

144

=12