Question

find the two numbers whose product is 135 and the ratio of differences of there squares to the sum of their square is 8:17.​

Answer 1

Answer:

The product of the two numbers is 16

Step-by-step explanation:

x²+y²=68

(x−y)²=36

x²−2xy+y²=36

x²+y²−x²+2xy−y²=68−36

2xy=32

2xy2=322

xy=16

xy=16

x-y=6

x=6+y

y(y+6)=16

y²+6y−16=16−16

y²+6y−16=0

(y−2)(y+8)=0

So y can either equal 2 or -8, and x can either equal -2 or 8.

Verifying:

8²+2²

=> 64+4=68

(−8)²+(−2)²

=> 64+4=68

(8)²−2(8×2)+(2)²

=> 64−32+4=36

(−8)²−2(−8×−2)+(−2)²

=> 64−32+4=36

xy=16

−8×−2=16

8×2=16

Thus the product of the numbers is 16.