Question

The difference of two natural number is180 .The squareof the smaller number is 8 times the larger number. Find the two number

Answer 1

let the 2 number be x the largest & y the smallest.

x^2 - y^2 = 180...........(equ.1)

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 , x = -10 (Not in negative)

so y^2 = 8x

y =√8x

y =√(8×18)

y =√144

y = 12

so the x and y are 18 & 12 respectively




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