Question

the difference of square of two number is 180. The square of the smaller number is 8 times the large number. Find the 2 number

Answer 1

let x be larger number and y be smaller number

then

$x {}^{2} - {y }^{2} = 180$

then

${y}^{2} = 8x$

put second equation in first

then first equation becomes

${x}^{2} - 8x = 180$

hence

${x}^{2} - 8x - 180 = 0 \\ (x - 18)( x + 10) = 0$

hence x=18 or x=-10

putting x=18 in second equation we get

y=12 but if we put x=-10 we get

${y}^{2} = - 80$

which is not possible

hence x=18 and y=12