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.

Quadratic equation​

Answer 1

Answer:

18,12

Step-by-step explanation:

Let us suppose two required is x and y.  

Such that x > y.

According to your given condition  

x^2 - y^2 = 180………………(1)  

And according to question  

y^2 = 8x. (Put this value in the above equation.)  

Then the above equation become  s

x^2 - 8x = 180.  

x^2 - 8x -180 = 0 (it is a quadratic equation)

x^2 -18x + 10x -180 = 0.  

x(x - 18) + 10(x - 18) = 0

(x + 10)(x - 18) = 0  

Here x has two values -10 and 18.(put these two value of x in equation (1) separately and then evaluate the value of y.and compare with the value of x to satisfy x > y.

That value of y is acceptable which less than x.

When x = -10.

100 - y^2 = 180

100 - 180 = y^2  

y = √(-80) (it is not acceptable)

When x = 18  

324 - y^2 = 180  

y^2 = 144 y = 12 (this value is acceptable.)

Hence,

the larger number is 18 and the smaller number is 12.

Hope it helps...

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Answer 2

Step-by-step explanation:

let the bigger no. is x

smaller no. is y

so. x²-y²=180

from second condition y²=8x

replacing y² by 8x

we get

x²-8x=180

x²-8x-180=0

x²-18x+10x-180=0

x(x-18)+10(x-18)=0

(x-18)(x+10)=0

so x=18

bigger no is 18