Question

sum of the two numbers is 55/22 and the product of that number is1 then what will be the sum of squares of that numbers​

Answer 1

Answer is 17/4

Solution

Let a and b be two nos

Given that a+b=55/22 =5/2

And ab=1

Then from (x+y)²=x²+y²+2xy

(5/2)²=a²+b²+2(1)

25/4=a²+b²+2

17/4=a²+b²

Answer 2

Answer

M² + N² = 17/4

$\rule{200}2$

Given that, sum of two numbers is 55/22.

Let us assume that, one number is M and other number is N.

So, their sum is written as M + N.

According to question,

$\implies\:\sf{M+N\:=\:55/22}$.....(1)

Also given that, product of that numbers is 1. Means, product of assumed numbers i.e. M and M is 1.

$\implies\:\sf{MN\:=\:1}$.......(2)

We have to find the sum of squares of the assumed numbers.

Used identity: (a + b)² = a² + b² + 2ab

$\implies\:\sf{(M+N)^2\:=\:(M)^2+(N)^2+2MN}$

Substitute the known values

$\implies\:\sf{(55/22)^2\:=\:(M)^2+(N)^2+2(1)}$

$\implies\:\sf{(5/2)^2\:=\:(M)^2+(N)^2+2}$

$\implies\:\sf{25/4\:=\:(M)^2+(N)^2+2}$

$\implies\:\sf{25/4\:-\:2\:=\:(M)^2+(N)^2}$

$\implies\:\sf{(25-8)/4\:=\:(M)^2+(N)^2}$

$\implies\:\sf{17/4\:=\:(M)^2+(N)^2}$