Question

the difference of squar of two number is 180 .The square of the smaller number is 8 times the large number . Find the two number​

Answer 1

Answer:

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 above equation.)

Then above equation become

x^2 - 8x = 180.

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

We can write as

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 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,

larger number is 18 and smaller number is 12.

Answer 2

Step-by-step explanation:

let take any two number x and y

1st condition,

x²-y²=180____(1)

y²= 8x___(2)

from 1 and 2 euation

x²-y²+y² = 180 +8x

x²-8x -180=0

x²+10x -18x -180=0

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

(x-18)(x+10)

x=18 and x=-12

from eq 2

y²= 8×18

y=12