Question

please answer step by step

Answer 1

let the second number be x. it is said that the difference between first number and x should be same as the difference between x and third number . Let's take this common difference as y. then first number is (x-y) and third number is (x+y).(y is positive).It is clearly given that the product of two smaller numbers is 85 therefore x(x-y)=85=>
${x}^{2} - xy = 85...(1)$
and the product of two larger numbers is 115 therefore x(x+y)=115=>
${x}^{2} + xy = 115...(2)$
Add (1)and (2)equations , we get
$2 {x}^{2} = 85 + 115 = 200 = > {x}^{2} = 100$
=> x=10 . Substitute x=10 in equation(1)=> then we get 100-10y=85=>10y=100-85=15=> y=1.5 So the numbers are 8.5,10 and 11.5
(OR)
=> x= -10. Substitute x=10 in equation(1) we get 100+10y=85=> y=85-100/10 = -15/10= -1.5 .So the numbers are -8.5, -10 and -11.5 .Hope it helps you...