Question

the sum of the squares of two positive number is 185 and the sum of the larger and thrice the smaller is 35 find the larger of the two numbers​

Answer 1

let the two numbers be x, y. x>y

given x^2+y^2=185 ------(1)

and x+3y=35

x=35-3y---------(2)

substitute (2) in (1)

(35-3y)^2+y^2=185

1225-210y+9y^2+y^2=185

10y^2-210y+1040=0

y^2-21y+104=0

y=13, 8

but y=8 because x becomes Negative for y=13

so largest number x=35-24=11