Question

The sum Of Two numbers is 11 and sum of their squarw is 65. Find the numbers

Answer 1

Answer:

So two no. are 4 and 7.

Step By step Explanation:

let the first no is x

So the second no is (11-x)

According to question  

x^2+(11-x)^2=65

x^2+121+x^2-22x=65

2x^2-22x+56=0

divide the equation by 2

x^2-11x+28=0

x^2-7x-4x+28=0

x(x-7)-4(x-7)=0

(x-7)(x-4)=0

(x-7)=0

x=7

(x-4)=0

x=4

So the No are 4 and 7  (Answer)

Answer 2

x+y=11....(1)

x2+y2=65....(2)

x=11-y [from 1]

Putting value of x in 2

(11-y)^2+y2=65

121+y2-22y+y2=65

2y^2-22y-56=0

y2-11y-28=0

y2-7y-4y-28=0

y(y-7)-4(y-7)=0

y=7 or y=4