Question

The sum of the squares of two natural no.S is 34 and the sum of 5 times the smaller and 3 times the larger os 30.Then nos are

Answer 1

Answer:

3  & 5

Step-by-step explanation:

let say number are

x. and y

x^2 + y^2 = 34

5x + 3y = 30

x = (30 - 3y)/5

((30-3y)/5)^2 + y^2 = 34

900 + 9y^2 - 180y + 25y^2 = 34*25

34y^2 -180y +900-850=0

34 y^2 -180y + 50 = 0

17y^2 -90y + 25 = 0

17y^2 -85y -5y + 25 =0

17y(y-5)-5(y-5)=0

(17y-5)(y-5)=0

y = 5   as  5/17 is not natural number

putting y into

5x + 3y = 30

5x +15 = 30

x = 3

so 3 & 5 are numbers