Question

Q1.Mean proportional of m
and n is 14. if m+n=53, then (m,n) is​

Answer 1

Explanation:

Given

Mean proportional of m and n is 14 also ,m+n= 53

To Find

We have to find m,n

$\sf\huge {\underline{\underline{{Solution}}}} </p><p>Solution$

Mean proportional of m and n = m:n::n:m

=> m*m= n²

Now,it is given that m+n= 53

Substitute the value of m or n from given input

=> m= 53-n------(1)

From equation 1

=> m²=n²

=> (53-n)²=n²

Identity: (a-b)²=a²+b²-2ab

=>(53)²+n²-2(53)(n)=n²

=> 2809+n²-106n= n²

n² lies on both sides so,it gets automatically cancelled

=> 2809-106n=0

=>-106n= -2809

=>106n= 2809

n= 2809÷106= 26.5

n= 26.5

Put n into equation 1

m= 53-n

=>m= 53-26.5

=>m=26.5

m= 26.5

∴ (m,n)= 26.5

Extra information=>

If x,y,z values having same quantities are said to be in proportion.

If y are in continued proportion then x,y,z are said to be in mean proportional.

____akansh__