Question

Hello...The sum of two natural no.s is 12 and the sum of their squares is 74 .Find the no.s.

Answer 1

Answer:

if y=7, x=5

if y=5,x=7

Step-by-step explanation:

let first and second no be x and y respectively

x+y=12

x²+y²=74

x=12-y

(12-y)²+y²=74

144-24y+y²+y²=74

2y²-24y+144-74=0

2y²-24y+70=0

y²-12y+35=0

y²-5y-7y+35=0

y(y-5)-7(y-5)=0

(y-7)(y-5)=0

y=7 and y=5

if y=7, x=5

if y=5,x=7

Answer 2

Answer:

x=5 y=7 , x=7 y=5

Step-by-step explanation:

Let the two natural no. be = x and y

x + y = 12. .....(I)

x² + y² = 74

(x + y) ² = x² + y² + 2xy

(12)² = 74 + 2xy

144 = 74 + 2xy

2xy = 144 - 74

2xy = 70

xy = 35

x = 35/y. .... (II)

put the value of x in eq I

x + y = 12

35/y + y = 15

35 + y² = 12 y

y² - 12y +35 = 0

y² -7y - 5y + 35 = 0

y(y-7) - 5(y-7) =0

(y-7)(y-5) =0

y=7

y=5

put the values of y in eq ii

I'd y=7

x=35/y

x=35/7

x = 5

if y=5

x=35/5

x=7