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:

${x}^{2} + {y}^{2} = 180 \\ {y}^{2} = 8x \\ {x}^{2} + 8x - 180 = 0 \\ {x }^{2} + 18x - 10x - 180 = 0 \\ x(x + 18) - 10(x + 18) = 0 \\ (x + 18)(x - 10) = 0 \\ x = - 18 \: and10 \\ {y}^{2} = 8 \times 10 \\ y = \sqrt{80} \\ andy = \sqrt{8 \times - 18}$

Answer 2

Answer:

The numbers are 18,-10

Step-by-step explanation:

let the larger number be x and the smaller be y

according to question

x2 +y2=180

also y2=8x

x2+8x-180=0

x=-b+√b2-4ac and x=-b-√b2-4ac

using this we get the answer

x=18,-10