Question

If (m+n) : (m-n) =7 : 3,then find the value of
(m²-n²) : (m²+n²) is : ??

Answer 1

given, (m + n)/(m - n) = 7/3

or, 3(m + n) = 7(m - n)

or, 3m + 3n = 7m - 7n

or, 3n + 7n = 7m - 3m

or, 10n = 4m

or, 5n = 2m

or, m/n = 5/2 ......(1)

now, (m² - n)² : (m² + n)²

= (m² - n²)/(m² + n²)

= {m²/n² - n²/n²}/{m²/n² + n²/n²}

= {(m/n)² - 1}/{(m/n)² + 1}

from equation (1),

= {(5/2)² - 1}/{(5/2)² + 1}

= {5² - 2²}/{5² + 2²}

= {25 - 4}/{25 + 4}

= 21/29

hence, (m² - n²) : (m² + n²) = 21 : 29

Answer 2

Answer:

21:29

Step-by-step explanation:

From the above given data, we can see that,

(m+n):(m-n)=7:3

Since ratio is comparing two quantities of same unit, we can write the above sum in this form:

(m+n)             7

_______ =    _

(m-n)              3

Or, 3m + 3n = 7m -7n (By simply  cross multiplying left hand side with right hand side)

Or, 10n = 4m

Or, m/n = 5/2 [By dividing 10/4 with 2 ]. ( Equation 1)

Now, according to the problem we have to find the value of :

(m²-n²)

_______

(m²+n²)

So, by diving both the numerator and denominator by n^2 we get:

(m²/n²-1)

__________

(m²/n²+1)

Now putting the value of m/n from equation 1, we get:

(5/2)²-1

__________

(5/2)²+1

By solving the squaring 5 and 2 we get:

(25/4)-1

_________

(25/4)+1

Now taking 4 as L.C.M we are solving both the numerator and denominator :

21/4

_____

29/4

So , by simplifying the above form we get :

21/29 or  21:29